THE  ]  [BRARY 


THE  UNIVERSITY 


OF  CAL  [FORNIA 


LOS  ANGELES 


SOUTHERN    BRANCH 

UNIVERSITY  OF  CALIFORNIA 
LIBRARY 

LOS   ANGELES.  CALIF. 


OF 


EARL  A.  SALIERS,  PH.D. 

Assistant  Professor  of  Accounting,  Sheffield 
Scientific     School    of     Tale     University 


(Fourth  Printing) 


NEW  YORK 

THE  RONALD  PRESS  COMPANY 
1918 


Graduate  School  of  Business  Admlnl8$raW<» 

f  California 
?.4,  California 


COPYRIGHT  1915 

by 
THE  RONALD  PRESS  COMPANY 


William  G.  Hewitt  Press,  Brooklyn,  Printers 
J.  P.  Tapley  Co.,  New  York,  Binders 


Bus.  Admin. 
Library 

"HF 
5681 

D5S 


Co  mj>  latter  anB 

this   book  is   most  affectionately 

dedicated  in  appreciation  of  their 

steadfast  interest  in  my  work 


PREFACE 

The  general  subject  of  depreciation  has  recently  been 

given    much    attention    by    accountants,    engineers,    and 

others  interested  in  the  financial  and  mechanical  problems 

of  modern  corporate   enterprise.      Vast  accumulations   of 

wealth  and  a  great  range  in  the  possibilities  of  investment 

have  necessitated  a  study  of  the  economics  of  business  with 

..     a  view  to  increased  efficiency,  safety,  and  justice  in  the  com- 

0-       plex  field  of  industry. 

In  this  book  a  study  is  made  of  the  depreciation  of  capi- 

[\      tal  values  which  in  their  manifold  forms  constitute  a  large 

U      share  of  the  world's  wealth.     Oftentimes  regarded  as  an 

abstract  and  theoretical  problem,  it  is  really  one  of  intense 

practicability.     In  the  nature  of  things  it  is  an  unavoidable 

•     problem,  and  any  objection  that  may  be  offered  on  the  score 

^     of  its  indefiniteness  is  outweighed  by  the  necessity  of  mas- 

cj     tering  it. 

The  depreciation  problem  may  be  viewed  from  two 
standpoints — that  of  the  accountant  and  that  of  the  engi- 
neer. The  engineer  deals  with  physical  conditions,  studies 
plant  deterioration,  the  necessity  of  replacement,  and  so  on. 
The  accountant  devises  ways  and  means  of  recording  in  the 
most  intelligible  manner  the  facts  in  connection  with  these 
changes.  The  work  of  the  two  should  be  correlated 
through  a  common  understanding  of  the  character  and  ex- 
tent of  depreciation.  The  engineer  having  shown  what  the 
rate  of  depreciation  is,  the  accountant  suggests  devices  for 
recording  it,  for  providing  replacement  funds,  etc.,  and  thus 
for  the  preservation  of  capital  value. 

Various  methods  have  been  suggested  as  suitable  for 
determining  the  annual  depreciation  charge.  Some  of 


vi  PREFACE 

these  require  computations  involving  the  use  of  algebraic 
formulas.  These  formulas  are  explained  fully,  and  illus- 
trated by  the  solution  of  problems  and  also  by  the  use  of 
graphic  charts.  It  is  thought  best  to  use  twenty-five  years 
as  a  period  sufficiently  long  to  indicate  clearly  the  effect  of  • 
interest  on  the  calculations,  and  at  the  same  time  not  too 
long  to  be  extraordinary. 

Much  literature  on  valuations  has  recently  appeared,  and 
while  no  pretense  is  made  at  giving  an  exhaustive  con- 
sideration of  that  subject,  it  is  believed  that  in  so  far  as 
depreciation  is  a  factor  in  valuations  a  tolerably  complete 
discussion  of  it  is  presented  here,  due  allowance  being  made 
for  the  somewhat  unsettled  condition  of  the  whole  subject. 

The  past  decade  has  witnessed  a  remarkable  extension 
of  governmental  supervision  of  industry.  An  attempt  is 
made  to  give  this  phase  of  the  matter  the  consideration 
which  its  importance  warrants.  The  legislatures  through 
their  laws,  and  the  courts  through  their  decisions,  exert  a 
great  influence — not  always  consistent  perhaps — in  the 
financing  and  managing  of  business  enterprise.  For  ex- 
ample, the  recently  enacted  income  tax  law  makes  it  quite 
necessary  for  business  men  to  study  the  depreciation  ques- 
tion carefully  in  order  to  report  intelligently  to  the  Gov- 
ernment While  much  space  is  given  to  this  new  phase  of 
the  situation,  this  is  justified  by  the  suddenness  with  which 
we  have  been  brought  face  to  face  with  it,  and  by  the  pros- 
*pect  of  its  future  permanence. 

EARL  A.  SALIERS 
Lehigh  University, 
May  1,  1915. 


CONTENTS 


PART    I— THEORY 

CHAPTER  PAGE 

I     CHARACTER  OF  INDUSTRIAL  PLANT      .        .       13 

Twofold  Character  of  Capital 

Corporate  Organization 

Corporations  Concentrate  Wealth 

Constituents  of  Plant  Value 

Direct  Costs 

Indirect  Costs  in  Valuations 

Recognition  of   Indirect  Costs  by  Interstate  Commerce 

Commission 
Engineering 
Preliminary  Expenses 
Insurance  During  Construction 
Interest  During  Construction 
Developmental  Costs 
Investment  vs.  Income 
How  the  Investor  is  Protected 
Depreciation 
Depreciation  Classified 
Unit  Depreciation 
Composite  Depreciation 
Preventing  Overcapitalization 
Functional  Depreciation 
Obsolescence 
Inadequacy 

Effective  Depreciation 
Depreciation  of  Indirect  Costs 
Proportion  of  Overhead  to  Direct  Costs 
The  Knoxville  Water  Case 
Mining  Companies,  Leases,  Patents 

II     ANALYSIS  OF  A  HYDROELECTRIC  PLANT        .       34 

Definition  of  a  Unit 
Analyzing  Cost  of  Industrial  Plant 
Analysis  of  Transmission  System 
Analysis  of  Power  House  Equipment 
Relation  of  Unit  Cost  to  Investment 

vii 


viii  CONTENTS 

CHAPTER  PAGE 

III  THE  PLANT  LEDGER 39 

Character  of  Plant  Ledger 

Description  of  Plant  Ledger 

Use  of  Plant  Ledger 

Adjustments  for  Obsolescence  or  Inadequacy 

Adjustments  for  Physical  Depreciation 

How  Plant  Ledger  is  Controlled 

Reserve  Indicates  Composite  Depreciation 

Relation  of  Reserve  to  Replacements 

The  Depreciation  Fund 

IV  DEPRECIATION  RESERVES  vs.  DEPRECIATION 

FUNDS 49 

Purpose  of  Depreciation  Charges 

Twofold  Object  in  View 

Reserves  and  Funds  Distinguished 

Sinking  Funds 

Depreciation  Funds 

Formation  of  the  Reserve 

Formation  of  the  Fund 

Terminology 

Advisability  of  Creating  Funds 

A  Study  of  Balance  Sheets 

V     DEPRECIATION  AND  EFFICIENCY  ...       60 

Relation  of  Depreciation  to  Efficiency 

City  of  Beloit  vs.  Beloit  Water,  Gas  and  Electric  Company 

Efficiency  Defined 

The  Factors  of  Value 

Depreciation — What  It  Is 

Comparison  of  Depreciation  and  Efficiency 

Investment  to  be  Preserved 

Efficiency  Not  to  be  Impaired 


PART    II— PRACTICAL   APPLICATIONS 
VI     REGULATION  BY  COURTS  AND  COMMISSIONS       66 

The  State's  Relation  to  Industry 
The  Importance  of  Accounts 


CONTENTS  ix 

CHAPTER  PAGE 

Meaning  of  "Net  Profits" 
Preservation  of  Capital 
Decisions  on  Depreciation 
Depreciation  a  Proper  Charge 
How  Depreciation  Charge  is  Regulated 
Regulations  of  Interstate  Commerce  Commission 
Purpose  of  the  Reserve 
Railroad  Companies 
Classification  of  Depreciation  Charges 
Industrial  Establishments 
Present  and  Future  Conditions 

VII     THE  INCOME  TAX 80 

The  Income  Tax  in  England 

English  Income  Tax  Decisions 

The  Income  Tax  in  the  United  States 

The  Corporation  Tax  of  1909 — Depreciation  Charges 

The  Corporation  Tax  of  1909 — Stocks,  Bonds,  and  Real 

Estate 

The  Income  Tax  of  1913 
Allowance  for  Exhaustion 
Stratton's  Independence,  Ltd.,  vs.  Howbert 
Interpretation  of  the  Income  Tax  Law 
How  Deduction  is  Limited 
Sale  of  Capital  Assets 
Good-Will 
Bad  Debts 

Reserve  for  Anticipated  Losses 
Removal  of  Buildings 
Incidental  Repairs 
Depreciation  Reserve 
Bonds 
Patents 
Timber  Land 
Natural  Deposits,  Coal,  etc. 

VIII     VALUATIONS 93 

State's  Relation  to  Industry 
Recent  Industrial  Changes 
Taxation  of  Public  Utilities 
Public  Utility  Service 
Public  Service  Commissions 


x  CONTENTS' 

CHAPTER  PAGE 

Growth  of  Commission  Regulation 
The  Valuation  Problem 
Depreciation  in  Valuations 
Present  Value  vs.  Cost  of  Reproduction 
Depreciation  as  Affecting  Basis  for  Rates 
Cost-of-Reproduction  Basis 
Cost-of-Reproduction-Less-Depreciation  Basis 
Equitable  Basis  of  Rate-Making 

Rates  Not  Made  Lower  When  Investment  is  Reduced 
Valuations  for  Purposes  Other  Than  Rate-Making 
Inadequate  Allowance  for  Depreciation 
Depreciation  Found  on  Basis  of  Averages 
Appreciation 

IX    LAND  IN  VALUATIONS         .        .        .        .     112 

Land  Not  a  Wasting  Asset 
Land  Values  That  May  be  Included 
Attitude  of  Courts 

Attitude  of  Interstate  Commerce  Commission 
Attitude  of  Minnesota  Commission 
Unusual  Interpretation  of  Cost-of-Reproduction 
Sales  Method 
Allowances  to  be  Made 
Appreciation  Considered  as  Income 
Appreciation  Limited  by  the  Supreme  Court 
Old  vs.  New  Value 

Reproduction  Method  Employed  on  Lehigh  Valley  Rail- 
road 
Land  Not  "Used  and  Useful" 


PART  III— DETERMINING  THE  DEPRECIATION 

CHARGE 

X     METHODS  OF  DEPRECIATION         .         .         .     120 

Depreciation  as  Affected  by  the  Point  of  View 

Cause  and  Effect 

Great  Accuracy  Impossible 

The  Straight  Line  Method 

The  Reducing  Balance  Method 


CONTENTS  xi 

CHAPTER  PAGE 

Interest 

The  Sinking  Fund  Method 
Interest  on  Investment — Annuity  Method 
The  Equal  Annual  Payment  Method 
The  Unit  Cost  Method 
Actual  Depreciation 

XI     THE  STRAIGHT  LINE  METHOD     .         .         .     134 

Characteristics 

The  Straight  Line  Formula 

Illustration  of  Straight  Line  Method 

Straight  Line  Tabulations 

Graphic  Illustration  of  Straight  Line  Method 

XII     THE  REDUCING  BALANCE  METHOD      .         .138 

Characteristics 

The  Reducing  Balance  Formula 

Illustration  of  Reducing  Balance  Method 

Reducing  Balance  Tabulations 

Graphic  Illustration  of  the  Reducing  Balance  Method 

XIII  THE  SINKING  FUND  METHOD      .         .         .     145 

Characteristics 

The  Sinking  Fund  Formula 

Illustration  of  Sinking  Fund  Method 

Sinking  Fund  Tabulations 

Graphic  Illustration  of  Sinking  Fund  Method 

XIV  THE  ANNUITY  METHOD      .         .         .         .152 

Characteristics 

The  Annuity  Formula 

Illustration  of  Annuity  Method 

Annuity  Tabulations 

Graphic  Illustration  of  Annuity  Method 

XV     THE  EQUAL  ANNUAL  PAYMENT  METHOD    .     159 

Characteristics 

Illustration  of  Equal  Annual  Payment  Method 

Equal  Annual  Payment  Tabulations 

Graphic  Illustration  of  Equal  Annual  Payment  Method 


xii  CONTENTS 

CHAPTER 

XVI     THE  UNIT  COST  METHOD    . 

Characteristics 

The  Unit  Cost  Formula 

Illustration  of  Unit  Cost  Method 


PAGE 
1 66 


APPENDIX 
XVII     LOGARITHMS  AND  THEIR  USE      .         .         .     172 

Computing  Interest 

Principle  of  Logarithms 

The  Logarithm 

The  Characteristic 

The  Mantissa 

Finding  the  Logarithm  of  a  Number 

Finding  the  Number  Corresponding  to  a  Logarithm 

Finding  Powers  and  Roots  of  Numbers 


XVIII     SELECTED  BIBLIOGRAPHY 


185 


FORMS 

FORM 

1.  Plant  Ledger  (showing  distribution  of  depreciation)       .      42 

2.  Plant  Ledger  (showing  adjustment  of  value)    ...      43 

3.  Plant  Ledger  (showing  added  installation  and  readjust- 

ment of  value) 44 

4.  Curves  Showing  Progress  of  Uniform  Depreciation  and 

of  Diminishing  Efficiency     ......       63 

5.  Graphic    Illustration    of    Depreciation  —  Straight    Line 

Method 137 

6.  Reducing  Balance  Curve 143 

7.  Sinking  Fund  Curves 150 

8.  Annuity  Curves 158 

9.  Curves  Illustrating  Equal  Annual  Payment  Method        .  164 


Principles   of  Depreciation 

Part  I — Theory 


CHAPTER    I 

CHARACTER  OF  INDUSTRIAL  PLANT 

Twofold  Character  of  Capital 

Modern  methods  of  production  and  distribution  require 
the  investment  of  large  amounts  of  capital  in  the  form  of 
fixed  assets.  This  may  be  seen  by  a  glance  at  any  under- 
taking .of  an  industrial  nature.  Thus  a  factory  is  composed 
of  the  site,  the  buildings,  and  the  equipment  of  machinery 
and  tools.  Land,  ballasted  roadbeds,  ties,  rails,  rolling 
stocks,  station  houses,  etc.,  are  the  elements  which  enter 
into  the  material  equipment  of  a  railroad  company.  Capi- 
tal so  invested  constitutes  one  of  the  great  divisions  of 
wealth,  and  may  be  distinguished  from  another  form  of 
wealth  known  as  circulating  capital,  which  finds  representa- 
tion in  current  assets,  such  as  cash  and  merchandise.  The 
subject  matter  of  this  book  is  confined  entirely  to  a  con- 
sideration of  capital  invested  in  the  form  of  fixed  assets. 

Corporate  Organization 

Much  of  the  world's  wealth  is  piloted  through  produc- 
tive channels  by  the  agency  of  corporate  organization. 
Corporations  may  now  be  regarded  as  guardians  of  the 
people's  wealth,  and  presumably  are  financed  and  managed 
in  the  interest  of  the  stockholders,  the  creditors,  and  the 
public.  That  the  general  public,  or  the  consumers,  have  in 

13 


I4  PRINCIPLES     OF    DEPRECIATION 

many  instances  a  very  direct  interest  in  the  corporate 
organizations  by  which  they  are  served,  is  now  fully 
recognized. 

When  the  corporation  is  formed,  funds  are  secured  by 
assessments  upon  the  stockholders  or  by  the  sale  of  securU 
ties,  or  by  both,  and  these  are  expended  in  the  purchase  of 
the  properties — tangible  and  intangible — required  in  the 
particular  industry.  Although  the  stockholders  and  the 
bondholders  continue  to  be  the  owners  of  this  invested 
wealth,  the  control  of  it  passes  to  a  great  degree  into  the 
hands  of  a  board  of  directors  and  other  corporate  officials. 

Corporations  Concentrate  Wealth 

A  few  responsible  men  thus  acquire  control  of  a  largq 
amount  of  wealth,  representing  harvests  gleaned  from  wide 
fields.  Subjects  of  many  nations  are  sometimes  stock- 
holders of  the  same  corporations.  In  this  way  wealth  is 
concentrated  where  it  is  most  effective.  Promoters  and 
organizers  have  this  in  view.  The  promoter  interests  the 
investor,  secures  his  good  will  and  his  money,  and,  with 
the  latter,  assets  needed  in  the  projected  business  are  pur- 
chased or  constructed. 

Constituents  of  Plant  Value 

The  economic  status  of  a  beginning  corporation  is  some- 
what more  difficult  to  comprehend  than  that  of  an  older  one. 
For  a  time  it  exists  by  consuming  a  part  of  its  own  capital, 
while  normally  the  cost  of  existing  is  met  out  of  the  cor- 
poration's income.  So  the  investment  represents  more  than 
the  bare  cost  of  the  units  of  which  the  industrial  plant  is 
constituted.  There  is  an  additional  increment  of  value 
which  may  be  regarded  as  arising  from  the  peculiar  adapta- 
bility of  the  various  plant  units  when  considered  in  their 
relation  to  one  another,  and  thus  as  a  part  of  the  physical 


CHARACTER    OF    INDUSTRIAL    PLANT  T- 

»J 

value  of  the  plant;  or,  as  some  prefer,  it  may  be  regarded 
as  an  intangible  value.  It  results  from  the  various  pre- 
liminary and  incidental  costs  of  construction — surveys, 
legal  aid,  insurance,  taxes,  interest  on  capital,  alterations  of 
plans,  and  so  on.  Ordinarily  such  expenditures  are  charged 
to  revenue,  but,  during  construction,  as  well  as  for  a  time 
thereafter  known  as  the  educational  period,  they  represent 
proper  charges  to  capital. 

Omitting  details,  an  industrial  plant  may  be  described 
as  of  a  threefold  character,  consisting  of: 

1.  Plant,   therein  being  included  all  direct  costs,   as 

real  estate,  right  of  way,  etc.,  with  a  percentage 
added  for  engineering. 

2.  Equipment,  a  direct  cost  to  which  nothing  need  be 

added  for  overhead  except  possibly  a  small  per- 
centage for  installation. 

3.  Capitalized    general   expenditures,    including   legal 

services,  insurance,  taxes,  etc.,   incurred  during 
construction  and  usually  for  a  time  thereafter. 

The  capitalized  general  expenditures  are  in  the  nature 
of  indirect  or  overhead  costs,  and  if  not  known  are  usually 
estimated  as  a  percentage  on  cost  of  construction  of  plant 
and  equipment. 

Direct  Costs 

As  far  as  possible  all  costs  of  plant  and  equipment 
should  be  charged  to  the  account  representing  that  particu- 
lar unit  of  plant  in  question.  Consequently,  as  already  sug- 
gested, a  certain  amount  over  and  above  prime  cost  will  be 
included  in  the  account.  In  this  way  all  costs  are  accounted 
for,  except  those  of  a  general  character,  which  cannot  be 
charged  directly  to  any  particular  account,  being  incident 
.rather  to  the  plant  as  a  whole. 


j6  PRINCIPLES    OF    DEPRECIATION 

Indirect  Costs  in  Valuations 

In  valuing  public  utility  properties  it  is  usually  neces- 
sary to  make  reproduction  cost  the  basis  of  the  valuation. 
The  prices  of  the  plant  units  must  then  be  based  on  prime 
cost,  to  which  must  be  added  percentages  for  overhead  -or 
indirect  costs.  The  prime  cost  of  the  plant  is  but  a  part  of 
the  actual  reproduction  cost,  because  it  includes  the  direct 
cost  only,  and  does  not  include  indirect  cost.  Courts  and 
commissions  are  apt  to  underestimate  this  indirect  element 
of  cost.  Errors  and  accidents  are  contingencies  sure  to 
occur,  but  after  the  occasion  has  passed  they  are  often 
ignored  because  not  evident.  Nevertheless  they  are  a  part 
of  the  investment. 

Recognition   of   Indirect    Costs   by   Interstate    Commerce 
Commission 

The  Interstate  Commerce  Commission  in  its  classifica- 
tion of  expenditures  for  road  and  equipment,  recognizes  the 
validity  of  such  incidental  costs.  It  provides  an  account  for 
"Other  Expenditures,"  to  which  it  allows  charges  for 
organization  expenses,  including:  cost  of  printing  stocks 
and  bond  certificates,  cost  of  disposing  of  securities,  salaries 
of  general  officers  during  the  period  of  construction  and  of 
clerks  engaged  on  construction  accounting,  rent  and  repair 
of  general  offices,  office  expenses,  and  such  items  of  an  in- 
cidental or  special  character  as  cannot  be  charged  to  any 
other  account.1 

In  the  following  pages  an  analysis  will  be  made  of  the 
principal  indirect  costs  of  industrial  plant.  An  under- 
standing of  them  is  essential  to  the  determination  of  plant 
value,  and  consequently  to  a  thorough  understanding  of  the 
principles  involved  in  the  solution  of  the  depreciation 
problem. 


1  Classification  of  Expenditures  for  Road  and  Equipment,  page  27. 


CHARACTER    OF    INDUSTRIAL    PLANT  lj 

Engineering 

This  division  of  cost  varies  widely  in  different  enter- 
prises as  well  as  in  different  localities.  It  is  low  where  an 
inferior  grade  of  talent  can  be  employed,  and  high  where 
the  best  grade  of  service  is  demanded.  In  case  of  railroads 
it  is  usually  in  the  neighborhood  of  5 %  of  the  cost  of  con- 
struction. This  was  the  percentage  used  in  the  recent  valua- 
tion of  the  Lehigh  Valley  Railroad.  It  must  be  remem- 
bered that  the  term  construction  cost,  as  here  used,  does 
not  include  cost  of  land  for  roadbed  or  other  purposes. 
This  accords  with  the  requirements  of  the  Interstate  Com- 
merce Commission,  as  indicated  in  primary  accounts  2  and 
3  of  their  classification  of  expenditures  for  road  and 
equipment. 

Engineering  costs  comprise  the  salaries  of  engineers 
and  assistants,  and  their  traveling  expenses  while  on  duty; 
also  the  cost  of  the  various  instruments  used — transits,  tape 
lines,  etc.  Of  an  investment  of  $26,736,000  in  the  Metro- 
politan Water  Works,  Boston,  7.77%  represented  engi- 
neering expenses,  preliminary  and  constructional.  Of  the 
disbursements  on  the  New  York  water  works  to  the  end  of 
September,  1913,  9.78%  of  the  total,  or  $10,050,000,  was 
for  engineering;  but  costs  of  extensive  boring  and  investi- 
gations were  here  included  which  were  not  included  in  the 
Metropolitan  Water  Works.  In  the  Boston  subways  the 
engineering  cost  ranged  from  5.05  to  9.88%  of  the  total 
cost  in  different  divisions  (1895-1912)  ;  in  the  Kennebec 
New  Gravity  Water  Supply,  6.69%  (1906)  ;  in  the  Louis- 
ville sewerage  works,  9%  (1906-1912)  ;  in  the  Springfield, 
Massachusetts,  water  works,  10%  (1910)  ;  and  in  the 
Springfield,  Massachusetts,  Ludlow  filters,  17%  (1906). 

Preliminary  Expenses 

Before  a  plant  is  brought  into  actual  existence,  to  say 


jg  PRINCIPLES     OF    DEPRECIATION 

nothing  of  putting  it  on  a  going-concern  basis,  a  more  or 
less  extended  period  transpires  during  which  the  work  of 
promoting  and  financing  is  being  done.  Surveys  may  be 
required  to  determine  whether  a  suggested  situation  is 
feasible  for  the  proposed  plant.  Then  the  consent  of  the 
landowners,  in  the  form  of  options,  must  be  obtained. 
These  and  similar  activities  necessitate  the  employment  of 
legal,  engineering,  and  financial  experts.  If  the  reports 
warrant  it,  a  charter  of  incorporation  is  obtained,  securities 
are  offered  for  sale,  the  land  is  acquired,  the  final  surveys 
are  made,  and  the  plans  and  specifications  for  the  proposed 
works  are  completed.  If  further  consideration  of  the  pro- 
posed site  is  not  justified  by  the  first  researches,  it  is  aban- 
doned for  a  more  promising  one ;  not,  however,  before  con- 
siderable money  has  been  spent,  which  must  form  a  part 
of  the  total  investment. 

Insurance  During  Construction 

This  is  primary  account  45  in  the  classification  of  ex- 
penditures for  road  and  equipment  prescribed  by  the 
Interstate  Commerce  Commission.  The  cost  of  insuring 
property  during  construction  and  until  the  plant  is  placed 
on  a  going-concern  basis,  should  be  charged  to  this  account, 
not  as  expense,  but  as  investment.  During  the  period  of 
construction  a  certain  amount  of  property  is  inevitably  de- 
stroyed by  accident  or  otherwise,  even  though  due  care  is 
used  to  protect  it.  For  the  same  reason  that  insurance  is  a 
legitimate  expense  in  a  going  concern,  its  cost  during  con- 
struction becomes  a  part  of  the  investment. 

Interest  During  Construction 

This  is  a  large  item  of  cost  and  deserves  careful  consid- 
eration. The  money  required  must  be  secured  sufficiently 
in  advance  of  the  time  when  it  will  be  needed,  to  avoid  a 


CHARACTER    OF    INDUSTRIAL    PLANT  IO, 

possible  stringency  in  the  funds  with  consequent  suspension 
of  work  and  loss.  Thus  interest  must  be  paid  on  the  money 
for  a  considerable  time  in  advance  of  its  disbursement,  as 
well  as  after,  and  at  a  rate  somewhat  higher  than  can  be 
had  by  placing  the  funds  with  depositaries  until  needed. 
However,  to  the  extent  that  interest  thus  received  offsets 
interest  paid,  to  that  extent  is  the  total  cost  reduced. 

Interest  cost  during  construction  is  ordinarily  computed 
as  equivalent  to  the  interest  on  the  total  cost  of  construction 
(not  including  interest)  for  one-half  the  period  of  construc- 
tion. This  method  is  based  on  the  assumption  that  the  rate 
of  expenditure  remains  constant  from  an  investment  of 
zero  to  an  investment  of  100% ;  also  that  interest  is  in- 
curred on  the  money  only  after  it  is  disbursed.  Such  an 
assumption  underrates  the  interest  cost,  and  unless  allow- 
ance is  made  for  the  higher  rate  of  interest  demanded  for 
money  to  be  invested  in  new  and  speculative  enterprises, 
the  actual  investment  is  still  further  underestimated. 

A  constant  rate  of  expenditure  on  plant  from  the  incep- 
tion to  the  completion  of  the  work  would  indeed  be  excep- 
tional. At  times  it  is  greater,  and  at  other  times  less,  than 
such  an  assumption  implies.  During  the  first  half  of  the 
period  of  construction,  when  most  of  the  materials  are  pur- 
chased, it  is  usually  greater,  with  a  resulting  excess  of 
interest  cost  over  that  implied  by  the  foregoing  theory. 
Interest  during  construction  is  paid  out  of  capital  and  is  as 
much  a  part  of  the  investment  as  cost  of  machinery  or 
buildings.  Consequently  interest  during  construction,  just 
as  insurance  on  buildings,  should  be  capitalized. 

Developmental  Costs 

Some  time  passes,  after  construction  is  completed,  be- 
fore the  business  reaches  a  profitable  basis.  During  this 
period  the  expenses  of  an  operating  concern  are  incurred, 


20  PRINCIPLES    OF    DEPRECIATION 

and,  owing  to  the  lack  of  sufficient  revenue,  must  be  paid 
out  of  capital.  This  necessitates  a  larger  investment  than 
would  otherwise  be  the  case,  though  not  evidenced  by  any 
addition  to  the  tangible  assets.  Investments  in  construction 
come  largely  to  a  standstill  with  the  beginning  of  this  edu- 
cational period,  but  current  expenses  and  interest  continue, 
and  add  an  additional  item  to  the  investment.  As  gross 
revenue  increases,  a  larger  and  larger  amount  of  it  can  be 
used  to  meet  these  obligations,  and  consequently  smaller 
and  smaller  charges  to  capital  will  be  made,  until  invest- 
ment on  this  score  ceases  altogether. 

Of  course  some  limitation  must  be  placed  on  the  devel- 
opmental period  in  any  case,  even  though  revenues  do  not 
increase  as  anticipated.  Capitalization  of  expenses  cannot 
be  indefinitely  continued,  for  the  possibility  of  ever  earning 
a  return  on  the  investment  would  grow  more  and  more 
remote,  and  in  case  of  public  service  corporations  would 
require  excessive  charges  on  the  service.  Some  enterprises 
are  by  nature  losing  ventures,  and  the  prolongation  of  the 
experimental  period  and  consequent  capitalization  would 
constantly  widen  the  chasm  between  actual  income  and  a 
satisfactory  return  on  the  investment.  These  principles 
apply  to  normal  properties.  If  the  venture  is  a  losing  one, 
whether  subject  to  commission  control  or  not,  the  investor, 
not  the  public,  must  suffer,  as  is  inevitable  in  the  field  of 
open  competition. 

Investment  vs.  Income 

A  thorough  knowledge  of  the  items  which  comprise 
investment  in  industrial  plant  is  of  increasing  importance. 
Formerly  competition  was  considered  the  chief  agent  de- 
termining income  on  investment.  It  was  thought  that  an 
investment,  whatever  its  amount  or  character,  receives  its 
equitable  reward  as  the  result  of  the  play  of  competition 


21 

forces,  much  as  water  finds  its  level  by  gravitation.  But 
the  experiences  of  the  past  decade  have  caused  us  to  alter 
our  notion  of  the  relation  of  income  to  investment.  Often- 
times competition  is  quite  impossible.  Many  of  our  public 
utility  companies  receive  franchises  granting  them  the  right 
to  operate  in  certain  districts  to  the  exclusion  of  all 
competitors. 

Under  such  conditions,  how  may  we  know  whether  an 
adequate  return  is  being  received  on  an  investment,  unless 
the  amount  of  the  investment  itself  is  carefully  calculated? 
And  it  is  but  natural  that  the  next  step  taken  is  to  regulate 
the  income  so  that  a  return  may  be  made  adequate  to  the 
protection  of  the  investor,  and  at  the  same  time  just  to 
the  consumer. 

How  the  Investor  is  Protected 

When  the  plant  enters  upon  its  career  of  activity,  if  it 
is  a  public  service  corporation,  it  is  subject  to  commission 
regulation,  and  probably  has  a  monopoly  of  the  market, 
thus  being  free  from  competition  of  similar  concerns.  It  is 
directly  controlled  by  a  board  of  directors  and  other  officers. 
Consumers  as  well  as  stockholders  and  creditors  have  inter- 
ests which  demand  protection.  If  it  is  a  private  corpora- 
tion, no  commission  will  stand  between  it  and  the  consumer, 
but  the  latter  protects  himself  by  bidding  in  the  open  mar- 
ket. When  the  single  proprietor  directly  supervised  his 
own  property  there  was  every  incentive  for  him  to  husband 
it  carefully.  Today,  however,  the  control  of  much  wealth 
is  entirely  lost  to  the  real  owner.  But  since  ownership 
implies  the  right  of  enjoyment  and  continued  possession, 
the  investor  must  look  to  the  corporation  officials,  or  to  a 
public  service  commission.  They  can  afford  protection  by 
pursuing  or  enforcing  sound  financial  methods. 

Good  accounting  is  based  upon  the  distinction  between 


22  PRINCIPLES    OF    DEPRECIATION 

capital  and  revenue.  The  integrity  of  all  investment  rests 
upon  this  principle.  Unless  it  is  adhered  to,  investment 
and  income  are  obscurely  merged.  As  a  result,  capital  is" 
frittered  away  as  dividends  and  the  financial  foundations 
of  the  company  are  weakened.  The  investment  must  be 
kept  undiminished  by  providing  for  its  renewal  or  replace- 
ment wherever  it  leaks  away  as  the  result  of  obsolescence, 
inadequacy,  or  decrepitude. 

Depreciation 
x 

This  loss  of  value,  whether  tangible  or  intangible  in 

form,  resulting  from  physical  decay,  or  from  obsolescence 
or  inadequacy,  which  indicate  functional  decay,  is  known 
as  depreciation.  It  necessitates  repairs,  renewals,  and  re- 
placements. Did  it  not  occur,  every  outlay  on  plant  would 
add  to  the  investment.  Depreciation  does  not  result  from 
one  cause  but  from  many  causes,  which  sometimes  leads  to 
the  belief  that  it  cannot  be  scientifically  cared  for.  But 
some  adequate  method  of  handling  it  is  not  merely  desir- 
able, but  necessary,  to  a  solution  of  problems  arising  in  the 
valuation  of  public  utility  properties,  and  in  the  manage- 
ment of  industrial  enterprises  generally. 

Differences  in  depreciation,  not  only  in  unlike  proper- 
ties, but  in  those  of  identical  construction,  frequently  occur. 
A  machine  constantly  exposed  to  the  damaging  influence  of 
the  elements,  even  if  little  used,  depreciates  rapidly.  The 
same  machine  adequately  sheltered  may  be  operated  con- 
stantly with  but  slight  deterioration.  One  machine  may  be 
so  constructed  that  ordinary  use  wears  it  slowly,  and  it  may 
become  obsolete  long  before  it  is  worn  out.  Another  de- 
teriorates rapidly  in  strength,  leaving  little  chance  of  ever 
becoming  obsolete.  Instruments  under  constant  or  unusual 
strain  wear  rapidly.  With  a  certain  amount  of  experience 
it  is  usually  possible  to  forecast  with  tolerable  accuracy  the 


CHARACTER    OF    INDUSTRIAL    PLANT  23 

date  of  physical  decrepitude,  but  it  is  more  difficult  to  pre- 
dict possible  future  obsolescence  or  inadequacy. 

Depreciation  Classified 

In  this  book  depreciation  will  be  understood  to  compre- 
hend all  losses  arising  out  of  physical  or  functional  decay, 
excepting  such  as  may  be  compensated  for  by  current  re- 
pairs. Depreciation  may  be  thought  of  as  affecting  the 
various  units  composing  plant,  or  as  affecting  the  whole 
plant.  Depreciation  may  therefore  be  classified,  according 
to  viewpoint,  into  unit  depreciation,  which  is  the  decay  of 
individual  machines  or  other  units  of  plant,  and  composite 
depreciation,  which  is  the  resultant  effect  upon  the  whole 
plant  of  unit  depreciation.  Total  depreciation  of  plant  is 
therefore  the  composite  depreciation,  which  is  equal  to  the 
sum  of  the  unit  depreciations  at  any  time. 

There  is  this  difference,  however,  between  unit  and  com- 
posite depreciation:  that  whereas  unit  depreciation  gradu- 
ally increases  from  zero  to  approximately  100%  of  the 
amount  originally  invested  in  the  units  of  plant,  composite 
depreciation  increases  from  zero  to  a  certain  percentage  of 
the  original  investment  in  the  entire  plant,  say  15  or  20%, 
beyond  which  it  is  prevented  from  going  because  of  the  con- 
tinuous replacement  of  wornout  or  obsolete  units  of  plant; 
but  can  never  be  entirely  extinguished,  except  in  the  ex- 
treme case  of  complete  replacement,  because  of  the  greater 
or  less  degree  of  depreciation  of  the  units  composing  the 
plant. 

Current  repairs  are  not  included  in  depreciation,  be- 
cause, with  the  exception  of  the  first  few  years  of  a  plant's 
life,  their  cost  is  spread  quite  evenly  over  the  accounting 
periods,  and  they  can  be  met  out  of  current  revenue  without 
affecting  the  equilibrium  of  the  investment.  Any  items  of 
so  large  an  amount  as  to  burden  the  year  in  which  they 


24  PRINCIPLES    OF    DEPRECIATION 

must  be  met,  cannot,  however,  be  classified  as  current  re- 
pairs, but  should  be  provided  for  under  the  head  of  depre- 
ciation. 

Unit  Depreciation 

Thus  parts  of  plant  must  sometimes  be  renewed  which 
would  be  an  unjust  charge  upon  current  revenue.  By  long 
use  they  have  lost  all  their  value  except  what  they  may  be 
worth  as  scrap.  Machines,  as  Karl  Marx  says,  are  con- 
gealed labor.  By  use  this  congealed  labor  has  been  ex- 
pended on  output  which  the  machine  assisted  in  producing. 
Or,  as  P.  D.  Leake  expresses  it,  the  capital  outlay  on  the 
machine  has  expired,  and  to  avoid  a  continual  diminution 
of  the  capital  outlay  on  the  whole  plant  it  must  be  replaced. 
When  a  machine  that  has  been  transferring  its  value  into 
commodities  for  twenty  years,  at  last  collapses,  it  ought 
not  to  be  replaced  out  of  current  revenue  unless  the  re- 
placements are  so  numerous  that  their  cost  would  be  evenly 
distributed  from  year  to  year.  Not  only  would  this  result 
in  an  unwonted  irregularity  in  apparent  net  profits,  but  to 
a  recent  buyer  of  stock  it  would  mean  a  charge  to  replace 
something  from  which  this  stockholder  has  derived  no 
material  benefit. 

It  is  therefore  proper  to  arrange  so  that  the  cost  of  a 
renewal  which  will  last  several  years  may  be  equitably 
charged  to  revenue  during  those  years,  instead  of  making 
the  entire  charge  to  current  revenue.  In  a  very  extensive 
plant  composed  of  many  and  varied  assets,  this  rule  may 
be  ignored,  for  there  renewals  are  quite  the  same  as  current 
repairs  in  a  smaller  plant,  and  become  evenly  distributed 
from  year  to  year.  When  such  is  the  case  it  is  not  im- 
proper to  charge  the  entire  cost  of  renewals  to  current 
revenue,  but  it  is  usually  better  tQ  differentiate  between 
these  two  classes  of  expense. 


CHARACTER    OF    INDUSTRIAL    PLANT  2c 

Composite  Depreciation 

Even  with  current  repairs  and  renewals  satisfactorily 
met,  the  investment  value  of  a  new  plant  will  continue  to 
decline  to  a  certain  point,  unless  counterbalanced  by  the 
unearned  increment  in  values  of  land,  or  strategic  location. 
It  is  better  not  to  offset  the  depreciation  of  wasting  assets 
by  the  unearned  increment,  even  if  there  is  a  certainty  of 
the  latter's  existence.  It  may  be  conservatively  omitted 
from  the  balance  sheet.  A  large  portion  of  every  plant, 
after  the  passage  of  twenty-five  years,  has  exhausted  a  con- 
siderable portion  of  its  useful  life,  the  extent  being  depend- 
ent on  the  character  of  the  individual  units  of  which  the 
plant  is  composed.  Not  all  parts  can  be  kept  entirely  new 
and  undepreciated.  Nor,  on  the  other  hand,  can  all  parts 
become  worn  out  or  obsolete  without  destroying  the  plant's 
efficiency.  During  the  early  years  of  the  plant's  life  no 
renewals  and  but  few  repairs  are  needed,  and  depreciation 
apparently  continues  unchecked.  When  repairs  and  re- 
newals do  become  necessary  they  do  not  bring  the  plant 
back  to  original  value,  but  merely  keep  it  from  becoming 
even  less  valuable.  On  first  thought  it  might  appear  that 
diminution  of  value  would  continue  until  normally  the  plant 
value,  being  represented  by  an  average  of  miscellaneous 
units  in  all  stages  of  depreciation,  would  be  approximately 
50%  of  cost  new.  Since,  however,  a  large  part  of  the 
investment  does  not  depreciate  at  all,  the  reduction  in  value 
will  probably  be  found,  ordinarily,  not  to  exceed  20  or  25% 
of  original  value. 

Preventing  Overcapitalization 

If  the  outstanding  stock  is  not  diminished  in  amount, 
the  net  result  of  this  composite  depreciation  is  overcapitali- 
zation, since  the  assets  no  longer  equal  their  former  value. 
Such  overcapitalization  may  be  prevented  in  two  ways: 


26  PRINCIPLES    OF    DEPRECIATION 

Either  the  capital  may  be  amortized  by  retiring  stock  to  an 
amount  equal  to  the  fall  in  values,  charging  the  cost  of  such 
retirement  to  revenue  and  thus  diminishing  permanently  the 
capital ;  or  a  replacement  reserve  may  be  created  to  offset 
this  unavoidable  decline  in  values,  in  which  case  capital  may 
be  retained  at  the  old  figure. 

This  replacement  reserve  may  be  employed  in  the  pur- 
chase of  additional  assets,  when  not  needed  for  specific  re- 
placements, and  still  the  transaction  will  be  essentially  a 
replacement.  Consequently  all  parts  of  the  plant  bought, 
up  to  the  limit  of  the  reserve,  will  be  divided  into  two 
classes:  (1)  actual  replacements,  and  (2)  units  which  are 
not  actual  replacements,  being  apparently  additions,  but 
which  are  essentially  of  the  character  of  replacements,  be- 
cause they  replace  values  lost  through  the  partial  deprecia- 
tion of  other  assets. 

As  it  is  customary  in  making  an  actual  replacement  to 
charge  the  depreciation  reserve  with  the  cost  of  the  item 
replaced  (see  Chapter  IV),  a  slight  complication  arises 
here,  because  no  specific  replacement  is  made,  and  it  would 
therefore  be  impossible  to  charge  the  reserve  with  the  cost 
of  any  particular  unit  of  plant.  The  reserve  would  there- 
fore remain  credited  with  the  full  amount,  and  be  charged 
only  when  a  unit  is  discarded  and  without  regard  to  the 
time  when  the  new  assets  which  replace  the  value  of  the  dis- 
carded unit,  were  purchased. 

Of  course,  if  assets  are  purchased  exceeding  in  value 
the  total  accrued  depreciation  indicated  by  the  reserve,  they 
are,  to  the  extent  of  the  excess,  extensions,  not  replace- 
ments. If  due  allowance  is  made  for  depreciation  accrued, 
the  distinction  between  replacements  and  betterments  will 
work  out  automatically  in  the  balance  sheet.  Thus,  if  the 
following  balance  sheet  represents  the  true  status  of  Com- 
pany A, 


CHARACTER    OF    INDUSTRIAL    PLANT 


BALANCE  SHEET  OF  COMPANY  A,  AS  AT. 


Plant $100,000 

Less  Reserve  for 
Depreciation..      20,000 


Cash 30,000 

$110,000 


Capital  Stock  Outstanding  $110,000 


$110,000 


then  the  following  balance  sheet  shows  the  situation  after 
an  apparent  addition,  but  in  reality  a  replacement,  has  been 
made: 

BALANCE  SHEET  OF  COMPANY  A,  AS  AT 


Plant $100,000 

Less  Re'serve  for 
Depreciation..      20,000    $80,000 


New  Building 20,000 

Cash 10,000 

$110,000 


Capital  Stock  Outstanding  $110,000 


$110,000 


The  $20,000  paid  for  the  new  building-  is  the  amount 
which  was  charged  to  gross  revenue  as  depreciation  cost 
when  the  reserve  for  depreciation  was  credited,  and  repre- 
sents a  return  of  the  investment  to  the  company,  that  much 
of  the  investment  having  gone  out  in  services  or  output. 
Had  it  been  employed  to  amortize  capital  instead,  the  bal- 
ance sheet  would  appear  thus: 

BALANCE  SHEET  OF  COMPANY  A,  AS  AT 


Plant $100,000 

Less  Reserve  for 
Depreciation..      20,000    $80,000 

Cash 10,000 

$90,000 


Capital  Stock  Outstanding  $90,000 


$90,000 


28 


PRINCIPLES     OF    DEPRECIATION 


Had  the  new  building  cost  $30,000,  it  would  be  partly 
a  replacement  ($20,000),  and  partly  a  betterment  ($10,- 
000),  since  $10,000  of  the  $30,000  of  cash  on  hand  repre- 
sents original  investment,  not  revenue  withheld  to  compen- 
sate for  depreciation.  The  balance  sheet  would  then  have 
appeared  as  follows,  although  the  amount  of  the  replace- 
ment and  of  the  extension  might  not  always  be  tabulated. 

BALANCE  SHEET  OF  COMPANY  A,  AS  AT.  ..... 


Plant  

$100,000 

Capital  Stock  Outstanding  $110  000 

Less  Reserve  for 
Depreciation.  . 

20,000    $80,000 

New  Building: 
Replacement.  . 
Betterment... 

$20,000 
10,000      30,000 

$110,000 

$110.000 

If  formed  by  equal  annual  charges,  the  depreciation  re- 
serve will  accumulate  rapidly  while  the  plant  is  still  new 
and  renewals  are  few,  and  should  be  sufficient  to  amortize 
capital,  as  suggested,  or  to  secure  the  replacement  of  de- 
creased asset  values  by  needed  improvements.  If  capital  is 
amortized,  the  charge  necessary  to  afford  a  fair  income  is 
lessened.  In  either  case  the  plant's  efficiency  should  actually 
increase,  since,  as  shown  later,  efficiency  may  remain  at 
practically  100%  even  where  there  is  considerable  deprecia- 
tion; while  depreciation  makes  it  possible  to  extend  the 
plant  to  a  certain  extent  without  increasing  the  investment. 

Functional  Depreciation 

Viewed  from  the  standpoint  of  cause  of  the  deprecia- 
tion rather  than  from  that  of  its  effect  on  plant  units  and 
composite  plant,  depreciation  may  be  again  classified  into 
functional  and  physical  depreciation.  Functional  deprecia- 


CHARACTER    OF    INDUSTRIAL    PLANT  29 

tion  results  from  the  obsolescence  or  the  inadequacy  of  a 
plant  unit,  or  a  combination  of  plant  units.  A  thing  is  obso- 
lete when  it  has  been  rendered  entirely  valueless  as  the  re- 
sult of  some  invention  or  discovery,  and  this  may  occur 
where  it  has  not  depreciated  at  all  physically.  A  thing  is 
obsolescent  when  its  value  is  being  reduced  by  inventions  or 
discoveries  but  has  not  yet  wholly  disappeared. 

Inadequacy,  on  the  other  hand,  indicates  that  a  thing  is 
incapable  of  fully  performing  the  function  for  which  it 
is  intended.  It  indicates  neither  physical  depreciation  nor 
obsolescence.  Inadequacy  may  result  from  expansion  of 
markets,  community  growth,  and  so  on. 

The  extent  to  which  the  service  may  be  cheapened  in 
case  of  obsolescence,  or  bettered  in  case  of  inadequacy,  by 
the  installation  of  a  new  plant  or  unit  of  plant,  determines 
the  amount  of  the  functional  depreciation  of  the  old  plant 
or  plant  unit.  It  must  be  written  down  to  such  an  extent 
that  the  production  cost  of  service  will  be  no  more  for  the 
old  than  for  the  new  plant. 

Obsolescence 

If  the  first  cost  of  the  old  and  the  new  plants,  respec- 
tively, be  added  to  the  capitalized  cost  of  operating  them, 
the  difference,  assuming  that  both  perform  the  same 
service,  represents  the  depreciation  of  the  old  plant  from 
obsolescence. 

If  the  first  cost  of  an  old  machine  was  $1,000,  and  its 
yearly  operating  expense  is  $200 ;  and  a  new  machine  which 
will  perform  the  same  total  service  as  the  old  one  will  do 
so  at  an  annual  operating  expense  of  $100,  and  a  first  cost 
of  $2,200,  then  if  money  is  worth  5%,  the  capitalized  cost 
of  operation  for  the  old  machine  is  $200  -r-  .05,  or  $4,000  ; 
and  for  the  new  machine,  $100-*- .05,  or  $2,000.  Adding 
these  to  the  first  costs,  we  have  for  the  old  machine : 


PRINCIPLES     OF    DEPRECIATION 

Original  cost $1,000 

Capitalized  operating  cost 4,000 


Total  capitalized  cost $5,000 

and  for  the  new  machine : 

Original  cost $2,200 

Capitalized  operating  cost 2,000 


Total  capitalized  cost $4,200 

The  value  of  the  old  machine  has  therefore  been  re- 
duced through  obsolescence  ($5,000  —  $4,200,  or  $800)  to 
a  present  value  ($1,000 —  $800)  of  $200;  $4,200  repre- 
sents the  highest  capitalized  cost  necessary  to  perform 
the  given  service.  If  a  machine  could  be  purchased  for 
$4,200  which  would  incur  no  operating  expenses,  the 
capitalized  cost  would  be  the  same  as  in  the  case  of  a 
machine  costing  $2,200  and  operated  for  $100  a  year,  and 
the  old  machine  would  still  be  worth  only  $200.  If  the 
old  machine  cost  $250  per  year  to  operate,  this  capitalized 
($250-^.05  =  $5,000 +  $1,000  =  $6,000)  would  exceed 
the  total  capitalized  cost  of  running  the  new  machine  by 
$1,800,  which  would  give  the  old  machine  a  minus  value  of 
$800,  and  a  yearly  saving  of  $800  X  .05,  or  $40,  would  be 
made  by  discarding  it  and  purchasing  the  new  one. 

Inadequacy 

Depreciation  due  to  inadequacy  may  be  found  on  the 
above  basis,  or  on  the  basis  of  the  capitalized  cost  of  pro- 
duction of  a  unit  of  output.  The  latter  may  be  the  better 
basis,  especially  if  more  than  one  old  unit  of  plant  is  re- 
quired to  do  the  same  work  one  new  one  will  do.  Thus,  if 
the  total  cost  of  producing  a  unit  of  output  by  the  old 
machine  is  $20,  and  by  the  new  machine  $18,  the  saving 
per  unit  is  $2.  If  the  number  of  units  of  output  produced 


CHARACTER    OF    INDUSTRIAL    PLANT  ^l 

annually  by  the  old  machine  is  100,  then  the  total  annual 
saving  is  $200.  $200  •*-  .05  =  $4,000,  which  sum  represents 
functional  depreciation  of  the  old  plant  and  the  amount 
over  and  above  the  depreciated  value  of  the  old  plant  which 
the  company  can  afford  to  pay  for  a  new  machine,  provid- 
ing the  old  one  can  be  disposed  of  at  its  depreciated  value. 

Effective  Depreciation 

Whichever  kind  of  depreciation — physical  or  functional 
— is  the  greater,  that  one  is  the  effective  one  in  determining 
unit  depreciation.  The  lesser  one  is  ineffective  and  should 
not  be  added  to  the  greater.  Some  units  of  a  plant  will  be 
influenced  more  by  functional  and  others  more  by  physical 
depreciation,  while  the  extent  of  depreciation  of  the  entire 
plant,  or  composite  depreciation,  will  be  the  resultant  of 
both  as  they  operate  upon  the  plant  units.  Total  composite 
depreciation  may  therefore  be  more  largely  the  resultant  of 
physical  or  of  functional  depreciation,  depending  upon 
which  affects  more  extensively  the  units  of  the  plant.  It 
would  rarely  be  made  up  entirely  of  one  to  the  exclusion  of 
the  other. 

Depreciation  of  Indirect  Costs 

We  have  seen  that  into  every  plant  there  must  enter 
certain  costs  of  an  indirect  character,  a  part  of  which  may 
be  apportioned  directly  to  the  units  of  plant,  but  the  re- 
mainder of  which,  being  of  a  general  character  incident 
rather  to  the  plant  as  a  whole,  must  be  charged  to  some 
capital  account  such  as  General  Expenditures.  If  these 
values  depreciate  along  with  the  material  assets,  allowance 
must  be  made  for  them.  On  the  other  hand,  if  the  benefits 
derived  from  them  are  of  a  permanent  character  they  need 
not  be  written  down.  Some  of  these  costs  are  purely  inci- 
dental to  the  constructional  and  educational  periods  and 


32  PRINCIPLES    OF    DEPRECIATION 

ordinarily  will  not  be  incurred  again.  The  costs  of  pre- 
liminary surveys  and  engineering,  and  of  at  least  a  part 
of  the  policing  and  contingencies  during  construction  and 
development,  will  remain  largely  or  wholly  non-depreciat- 
ing, except  in  case  of  mines  and  similar  properties  of  limited 
lifetime.  Interest,  taxes,  and  insurance  during  construction 
become  a  part  of  the  permanent  investment  if  not  again 
incurred. 

Proportion  of  Overhead  to  Direct  Costs 

These  overhead  charges  constitute  a  large  part  of  the 
investment,  ranging  from  20  to  40%  or  more  of  prime 
cost.  In  the  valuation  of  the  Lehigh  Valley  Railroad  they 
were  estimated  at  30.74%,  and  in  the  Buffalo,  Rochester  & 
Eastern  at  40.3%  of  prime  cost. 

The  Knoxville  Water  Case 

Reference  should  be  made  to  the  recent  change  which 
has  taken  place  in  the  attitude  of  the  courts  toward  com- 
panies engaged  in  various  industries,  growing  out  of  a 
better  understanding  of  the  character  of  industrial  plant. 
This  change  is  well  reflected  in  the  decision  of  the  Supreme 
Court  of  the  United  States  in  the  Knoxville  Water  Case.2 
Here  the  court  stated  definitely  that  before  any  question  of 
profit  can  be  raised,  not  only  current  repairs,  but  replace- 
ments and  depreciation,  must  be  made  good  out  of  earnings. 
No  company  must  have  its  properties  wasted  without  ade- 
quate provision  for  replacement.  The  original  investment 
must  not  be  diminished,  and  it  is  the  company's  duty  to 
security  holders  and  to  the  public  to  see  that  it  is  not.  The 
only  alternative  would  be  the  issue  of  new  securities  with 
consequent  overcapitalization,  followed  by  disaster  to  the 
business. 

"212  U.  S.  1. 


CHARACTER    OF    INDUSTRIAL    PLANT  33 

Mining  Companies,  Leases,  Patents 

Corporations  engaged  in  mining  are  exceptions  to  the 
rule  that  the  investment  must  be  kept  from  diminishing. 
There  is  good  authority  both  in  England3  and  the  United 
States4  for  the  distribution  of  the  proceeds  of  mining  opera- 
tions without  making  the  customary  retention  for  decrease 
in  value  of  the  mines  through  extraction  of  minerals.  The 
same  principle  applies  to  any  concern  utilizing  a  wasting 
asset — one  which  can  only  be  made  useful  by  being 
consumed. 


8  Lee  v.  Neuchatel  Co.,  41  Ch.  Div.  1. 

*  People  v.   Roberts,  156  N.   Y.   585 ;  see  Clark  on   Corporations,  pages  333,  334. 


CHAPTER    II 

.  ANALYSIS    OF   A    HYDROELECTRIC    PLANT 

In  the  preceding  chapter  the  general  characteristics  of 
industrial  plant  were  described.  In  practice  the  deprecia- 
tion problem  can  be  adequately  handled  only  by  first 
making  an  analysis  of  the  units  of  which  such  a  plant  is 
composed,  based  upon  their  use,  value,  and  longevity.  In 
this  chapter  such  an  analysis  will  be  made  of  a  hydro- 
electric plant  for  the  purpose  of  affording  an  illustration 
and  to  serve  as  subject  matter  for  further  discussion  of  the 
question  of  method  in  caring  for  depreciation. 

Definition  of  a  Unit 

The  word  "unit,"  as  used  in  this  and  the  following 
chapter,  will  be  understood  to  mean  a  subdivision  of  plant, 
consisting  of  one,  a  few,  or  even  many  items,  as  determined 
by  a  consideration  of  use,  value,  and  longevity;  the  unit 
in  each  case  being  the  most  suitable  portion  of  plant  to 
employ  as  a  basis  for  figuring  depreciation.  Thus  a  unit 
may  be  a  building,  or  twenty  locomotives  of  similar  class, 
or  a  steamboat,  or  the  hulls  of  ten  similarly  constructed 
steamboats,  and  so  on,  the  question  being  always  one  of 
expediency  and  determined  upon  the  actual  conditions. 
The  following  rules  may  be  of  assistance: 

1.  A  unit  of  plant  cannot  be  made  up  of  unlike  things, 
or  things  having  different  functions. 

2.  For  the  sake  of  the  saving  in  calculations,  a  unit 
should  include  as  many  items  as  possible  capable  of  being 
handled  together. 

3.  A  number  of  things  may  be  handled  together  as  a 

34 


ANALYSIS    OF    A    HYDROELECTRIC    PLANT         35 

unit  if  they  have  the  same  general  physical  make-up,  are 
employed  for  the  same  purpose,  and,  what  would  be  ordi- 
narily inferred  from  the  foregoing,  have  approximately  the 
same  lifetime. 

Thus  a  number  of  locomotives  of  a  given  type  would 
form  one  unit,  steel  rails  of  a  given  weight  another,  sta- 
tion house  of  a  given  structure  another,  water-wheels  of  a 
certain  pattern  another,  and  so  on. 

Analyzing  Cost  of  Industrial  Plant 

A  plant  generating  electricity  may  be  run  by  either 
steam  or  water  power.  The  fixed  charges  on  a  steam 
plant  being  much  greater  than  on  a  water  power  plant, 
the  economy  of  the  latter  makes  it  desirable  when  condi- 
tions are  such  that  its  use  is  possible.  Following  the  gen- 
eral classification  of  plant  values  given  on  page  15,  the 
component  parts  of  a  hydroelectric  plant  may  be  sub- 
divided as  follows:1 

TABLE  1 — SUBDIVISION  OF  COST  OF  INDUSTRIAL  PLANT 

Proportional 
I.  Plant:  Cost 

(a)  Riparian  rights  for  dam  and  flowage  basin,  real 

estate  expenses,  organization  expenses,  prelim- 
inary legal  expenses,  cost  of  financing,  removal 
of  railroads,  highways,  bridges,  and  all  expenses 
preliminary  to  actual  construction  of  work 20% 

(b)  Permanent  construction,   dam,  power  house  and 

waterways,  etc 30% 

(c)  Transmission  system : 

(1)  Right  of  way 4.5 

(2)  Copper  1.5 

(3)  All  else 7.0       13% 

IT.  Equipment: 

(a)  Equipment  of  power  house 14% 


1  The  data  on  hydroelectric  plant  used  in  this  chapter  are  taken  from  the  dis- 
cussions of  Calvert  Townley  and  Dr.  Gary  T.  Hutchinson,  before  the  American 
Institute  of  Electrical  Engineers,  December  30,  1909. 


^6  PRINCIPLES     OF    DEPRECIATION 

III.  Capitalized  General  Expenditures: 

(a)  General  expense,  engineering  administration,  legal, 

etc 11  % 

(b)  Interest  during  construction 12% 

Of  these  items  only  I-b,  I-c  and  Il-a,  comprising  57% 
of  the  entire  cost  of  the  plant,  are  subject  to  depreciation, 
and  of  item  I-b  a  large  part  does  not  depreciate  to  any 
appreciable  degree  from  physical  causes,  since  it  covers 
rock  excavation  and  concrete. 

Table  1  indicates  the  proportional  cost  of  the  main 
subdivisions  of  the  plant.  Thus  the  cost  of  the  equipment 
is  14%,  and  of  the  transmission  system  13%,  of  the  total 
cost  of  the  plant.  Tables  2  and  3  indicate  what  percentage 
the  cost  of  the  different  units  of  equipment  and  transmis- 
sion system  is  of  the  total  cost  of  the  equipment  and 
transmission  system,  respectively. 

Analysis  of  Transmission  System 

For  illustrative  purposes  our  attention  will  be  con- 
fined to  items  I-c  and  Il-a,  as  they  will  serve  to  indicate 
the  effects  of  both  functional  and  physical  depreciation. 
The  following  table  classifies  the  units  of  the  transmission 
system  (I-c),  indicating  the  proportional  cost  of  the  units 
and  their  lifetime  in  years.  In  this  connection  it  may  be 
well  to  repeat  that  by  unit  is  meant  one,  or  more  than  one, 
item  of  plant,  as  already  explained. 

TABLE  2 — COST  AND  LIFETIME  OF  TRANSMISSION  SYSTEM 

1.    TRANSMISSION  LINE 

Proportional    Life  in 


Cost 
45.0 

Year 

18.4 

is 

5.1 

10 

I-c-4    Insulators   . 

2.1 

10 

ANALYSIS     OF    A    HYDROELECTRIC    PLANT  ^ 

I-c-S     Copper  23.7  25 

I-c-6    Installation 5.7 


100.0 
2.    SUB-STATIONS 

Proportional    Life  in 

Cost  Years 

I-c-7    Land 6  • 

I-c-8    Buildings   30  25 

I-c-9    Transformers  40  20 

I-c-10  Switches,  etc 16  10 

I-c-1 1  Installation 8 

100 
Analysis  of  Power  House  Equipment 

The  equipment  of  power  house  is  classified  in  the  fol- 
lowing table: 

TABLE  3 — COST  AND  LIFETIME  OF  POWER  HOUSE 
EQUIPMENT 

Proportional    Life  in 

Cost  Years 
II-a-1     Stop  logs,  gates,  and  other  wood  exposed 

to  air  and  water 0.80  5 

II-a-2    Flooring,   roofing,  hardware,  and  miscel- 
laneous  fixtures. .  • 9.80  15 

II-a-3     Tile   wainscoting,   sewage,   plumbing  sys- 
tem, metal  window  frames,  etc 2.45  15 

II-a-4    Electric  light  and  telephone 0.80  10 

II-a-5     Switchboard  equipment 4.35  10 

II-a-6     Cables  and  heavy  wiring 3.90  10 

II-a-7    Cranes   1.25  15 

II-a-8    Water-wheels 33.75  25 

II-a-9    Water-wheel   governors 2.90  10 

II-a-10  Generators  and  transformers..  40.00  25 


100.00 

Relation  of  Unit  Cost  to  Investment 

If  the  cost  of  the  entire  plant  is  known,  the  cost  of 


38  PRINCIPLES     OF    DEPRECIATION 

any  unit  can  easily  be  derived  by  first  finding  what  per- 
centage the  chief  subdivision  of  which  the  unit  forms  a 
part,  is  of  the  cost  of  the  plant,  and  taking  this  percentage 
of  the  entire  cost  of  the  plant.  When  the  value  of  the 
chief  subdivision  is  thus  found,  the  value  of  the  unit  may 
then  be  determined  by  finding  what  percentage  the  unit  is  of 
the  chief  subdivision. 

To  illustrate,  if  the  cost  of  the  entire  plant  is  $100,000, 
then  the  cost  of  the  power  house  equipment  is  14%  of 
that  amount,  or  $14,000,  and  the  cost  of  any  unit  com- 
posing the  power  house  may  be  found  by  multiplying 
$14,000  by  the  percentage  of  the  cost  of  equipment  repre- 
sented by  it.  Thus  the  cost  of  the  water-wheels  is  .3375 
of  $14,000,  or  $4,725.  These  percentages  must,  of  course, 
be  based  upon  the  actual  cost  of  the  properties. 


CHAPTER    III 

THE    PLANT    LEDGER 

Character  of  Plant  Ledger 

The  "plant  ledger"  should  be  made  an  essential  part 
of  the  double-entry  books,  and  be  controlled  by  a  Plant 
account  in  the  general  ledger  with  which  it  must  be  in 
agreement.  The  form  and  arrangement  of  the  plant 
ledger  should  be  such  as  to  combine  brevity,  accuracy,  and 
compactness  with  the  necessary  amount  of  detail.  It 
should  afford  a  complete  record  of  the  life  of  each  unit 
or  class  of  units  of  the  plant.  In  determining  what  shall 
be  considered  a  unit  or  class  of  units,  an  analysis  of  plant 
similar  to  that  in  the  preceding  chapter  should  be  made. 

The  plant  ledger  must  show  not  only  the  original  in- 
vestment in  a  unit  of  plant,  but  also  in  all  additional  units 
of  a  like  character  afterwards  purchased.  It  must  show  as 
well  the  losses  sustained  each  year  on  all  wasting  assets 
and  their  resultant  diminished  value.  If  desirable,  the 
month  may  be  made  the  time  basis  for  figuring  deprecia- 
tion, but  in  most  cases  the  yearly  basis  will  be  sufficiently 
accurate,  and  is  employed  in  the  following  illustrations. 
The  plant  ledger  should  also  be  so  arranged  that  all 
needed  adjustments,  either  to  show  the  effect  of  func- 
tional depreciation,  or  that  of  an  unanticipated  shortening 
or  lengthening  of  a  unit's  life,  can  be  made. 

Description  of  Plant  Ledger 

A  loose-leaf  book  is  most  suitable  for  the  plant  ledger, 
because  it  is  unnecessary  to  carry  in  it  more  pages  or 
sheets  of  paper  than  are  needed  for  current  work,  and 

39 


40  PRINCIPLES     OF    DEPRECIATION 

additions  can  be  made  when  required.  Forms  1  to  3  repre- 
sent pages  of  the  plant  ledger.  An  explanation  of  the  data 
entered  in  these  forms  is  given  below. 

In  the  plant  ledger  the  pages  or  sheets  used  for  the 
record  of  any  unit  or  class  of  units  should  be  numbered' 
consecutively  to  prevent  confusion.  The  name  of  the 
unit  appears  in  the  upper  left-hand  corner.  The  year  of 
installation  of  a  new  unit,  or  of  adjustment  of  an  old  one, 
appears  in  the  first  column.  In  case  of  an  old  plant  it 
indicates  the  year  the  plant  ledger  was  installed.  In  the 
next  column  is  entered  the  estimated  life  (or  remaining 
life)  of  the  unit,  and  in  the  third  column  its  value  at  time 
of  installation.  In  the  remaining  columns  the  annual  de- 
preciation allowances  are  distributed,  their  total  equaling 
the  cost  or  adjusted  value  of  the  unit,  as  given  in  column 
three,  the  element  of  scrap  value  not  being  taken  into  con- 
sideration. 

The  first  distribution  column  of  any  particular  unit 
should  correspond  in  date  with  the  year  of  installation  of 
the  property.  Approximate  accuracy  will  be  secured  if 
for  the  first  year  the  distribution  allowance  be  calculated 
as  one-half  that  of  a  full  year,  since  the  installations  will 
be  fairly  well  scattered  through  it,  some  going  into  opera- 
tion early,  others  late,  in  the  year. 

If  a  number  of  items  of  a  class  are  installed  at  different 
times  during  the  year,  or  if  there  may  be  uncertainty  as  to 
whether  the  installations  for  the  year  in  any  particular 
class  are  completed,  an  auxiliary  blank  should  be  used 
from  which  at  the  close  of  the  year  a  recapitulation  can 
be  made  and  the  total  installation  entered  in  the  plant 
ledger.  In  this  way  one  line  serves  for  each  year's  in- 
stallations of  any  class,  and  the  work  of  computing  the 
annual  allowances  and  possible  future  adjustments  is 
reduced  to  a  minimum. 


THE    PLANT    LEDGER  4I 

Use  of  Plant  Ledger 

To  illustrate  the  working  of  the  plant  ledger,  we  may 
take  the  hydroelectric  plant  analyzed  in  the  preceding 
chapter,  assuming  its  total  investment  value  to  be 
$100,000,  and  selecting  one  of  its  units.  For  example, 
let  us  take  item  9  of  power  house  equipment,  "Water- 
Wheel  Governors,"  having  an  estimated  life  of  ten  years, 
and  comprising  2.9%  of  the  value  of  the  equipment,  or 
$406.  Assuming  the  installation  to  have  been  made  in 
the  year  1910,  the  entry  for  it  in  the  plant  ledger  is 
shown  in  Form  1.  As,  according  to  our  assumption,  but 
one-half  of  a  full  year's  depreciation  occurs  in  the  year  of 
installation,  the  distribution  of  the  depreciation  will  ex- 
tend over  eleven  columns  in  the  ledger,  a  similar  half- 
year's  charge  being  made  in  the  eleventh  column,  or  for 
1920. 

If  no  additional  installations  are  made;  if  functional 
depreciation  does  not  diminish  the  value  more  rapidly 
than  physical  depreciation;  and  if  our  estimate  of  the 
unit's  lifetime  has  been  correct,  or  nearly  correct,  no 
adjustments  will  be  required  except  the  annual  deduction 
of  the  depreciation  allowance  from  the  balance  brought 
forward  from  the  previous  year.  In  such  a  case  the  record 
of  this  unit,  when  it  has  become  worn  out,  appears  in 
Form  1. 

Adjustments  may  be  required,  however,  at  times  dur- 
ing the  lifetime  of  the  unit  for  either  of  two  reasons:  First, 
obsolescence  or  inadequacy  may  so  impair  the  functional 
value  of  the  unit  that  its  investment  value  drops  below 
what  the  plant  ledger  indicates.  Secondly,  with  the  pas- 
sage of  time,  it  may  be  found  that  the  lifetime  of  the  unit 
was  incorrectly  estimated,  necessitating  the  distribution 
of  its  remaining  value  on  a  new  basis,  as  illustrated  by  the 
problem  on  page  45. 


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PRINCIPLES    OF    DEPRECIATION 


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THE    PLANT    LEDGER 


45 


Adjustments  for  Obsolescence  or  Inadequacy 

Let  us  assume  that  in  the  year  1914  certain  causes 
lead  to  an  abrupt  fall  in  value,  resulting  from  functional 
depreciation,  the  reduced  value  of  the  unit  being  found  to 
be,  according  to  principles  stated  on  pages  29,  30,  $150. 
The  balance  brought  forward  for  the  year,  as  shown  in 
Form  2,  is  $263.90,  and  the  physical  depreciation  for  the 
year  is  $40.60,  leaving  $223.30,  or  $73.30  excess  over 
actual  value.  This  amount  must  therefore  be  deducted  as 
functional  depreciation.  Owing  to  this  extraordinary  de- 
duction, it  will  be  necessary  to  make  a  new  distribution 
over  the  remaining  years  of  the  olant's  life  on  the  basis  of 
the  remaining  value,  $150.  A  red  line  should  be  drawn 
through  the  future  distributions  on  the  basis  of  old  value 
and  a  new  distribution  made  on  the  next  line  below.  These 
alterations  are  shown  in  Form  2.  No  new  entry  is  made 
in  the  column  headed  "Original  Value,"  except  in  case  of 
purchase  of  additional  property. 

Adjustments  for  Physical  Depreciation 

If,  after  a  number  of  years,  experience  shows  that  the 
original  estimate  of  lifetime  was  in  error,  a  somewhat 
similar  adjustment  should  be  made;  not,  however,  by 
altering  the  amount  remaining  to  be  depreciated,  but  by 
extending  it  over  a  greater  or  less  number  of  years,  thus 
decreasing  or  increasing  the  remaining  annual  charges. 
Such  an  adjustment  is  shown  in  Form  3,  for  the  item  in- 
stalled in  the  year  1916. 

The  correctness  of  the  work  of  a  sheet  may  be  checked 
by  finding  the  total  of  the  future  distributions,  which 
should  be  equal  to  the  last  depreciated  balance. 

In  case  of  a  sudden  heavy  fall  in  values  due  to  func- 
tional depreciation,  its  deduction  in  the  revenues  of  the 
current  year  would  create  an  excessive  burden.  It  might 


46  PRINCIPLES     OF    DEPRECIATION 

then  be  well  to  spread  the  extra  charge  over  a  period  of, 
say,  two  or  three  years,  by  dividing  it  into  as  many  equal 
parts.  Thus  in  Form  2  the  functional  depreciation, 
amounting  to  $73.30,  would  be  divided  into  three  parts 
of  $24.43  each  and  deducted  over  the  three-year  period 
1914,  1915,  and  1916,  an  equal  amount  each  year. 

In  this  somewhat  extraordinary  instance  there  would 
be  a  difference  of  twice  $24.43,  or  $48.86 — the  amount 
not  deducted  in  the  current  year — between  the  depre- 
ciated balance  and  the  extensions  in  the  depreciation  col- 
umns; for  while  the  latter  are  based  entirely  on  the 
reduced  value  of  the  property,  the  former  has  not  been 
reduced  by  the  full  amount.  But  as  soon  as  the  full 
amount  of  the  functional  depreciation  has  been  deducted, 
the  two  will  again  be  equal. 

How  Plant  Ledger  is  Controlled 

As  suggested,  the  plant  ledger  is  controlled  by  the 
Plant  account  in  the  general  ledger.  Instead,  however, 
of  merely  agreeing  with  its  controlling  account,  as  is  usual 
with  subordinate  ledgers,  the  plant  ledger  should  be  in  a 
twofold  agreement  with  its  controlling  account;  or  per- 
haps it  might  be  expressed  by  saying  that  it  must  agree 
with  both  the  Plant  account  and  the  Depreciation  Reserve 
account.  For,  whenever  any  accounts  are  charged  in  the 
plant  ledger,  the  controlling  Plant  account  is  charged 
with  an  equal  amount,  the  only  difference  being  that  the 
charges  are  subdivided  in  the  plant  ledger  among  the 
proper  accounts;  whereas  their  total  is  carried  to  the  con- 
trolling account.  Likewise,  whenever  any  account  is 
credited  in  detail  in  the  plant  ledger,  which  is  done  only 
when  a  unit  of  plant  is  scrapped,  there  will  be  an  equal 
debit  made  to  the  Reserve  for  Depreciation  account  in 
the  general  ledger.  It  follows  that  while  the  first  cost  of 


THE    PLANT    LEDGER 


47 


all  existing  units  of  plant  is  shown  in  detail  in  the  plant 
ledger  and  in  total  in  the  Plant  account  in  the  general 
ledger,  the  actual  depreciated  value  is  indicated  by  the 
difference  between  the  Plant  account  and  the  Reserve 
for  Depreciation,  shown  best  in  the  balance  sheet  by  de- 
ducting the  latter  from  the  former,  as  explained  in 
Chapter  IV. 

Reserve  Indicates  Composite  Depreciation 

If  no  renewals  or  replacements  whatever  were  made  to 
the  plant,  the  continually  increasing  reserve  for  deprecia- 
tion would  indicate  the  growth  of  composite  depreciation, 
which  would  finally  consume  the  entire  value  of  the  plant. 
But  as  soon  as  they  are  needed,  renewals  are  made,  and 
after  a'  time  they  entirely  counterbalance  the  effects  of 
depreciation,  with  the  result  that  the  reserve  for  deprecia- 
tion indicates  the  extent  to  which  at  any  time  the  com- 
posite depreciation  of  the  entire  plant  has  progressed. 

Relation  of  Reserve  to  Replacements 

As  has  been  suggested  in  Chapter  I,  the  tendency  of 
composite  depreciation  to  reduce  plant  values  below 
original  investment  values  may  be  avoided  by  making 
additions  to  plant  to  the  extent  that  composite  depre- 
ciation is  not  covered  by  actual  renewals,  the  additions 
being  in  reality  replacement  of  values  lost  through  de- 
preciation. If  the  records  are  properly  kept  the  extent 
of  the  composite  depreciation  of  the  original  investment 
will  be 'at  all  times  indicated  by  the  depreciation  reserve, 
and  this  will  in  turn  serve  to  indicate  the  amount  which, 
may  be  invested  in  additional  plant  when  it  is  not  needed 
in  actual  replacements.  It  must  be  remembered,  however, 
that  reserve  for  depreciation  is  not  changed  by  such  addi- 
tions, being  reduced  only  when  old  units  are  scrapped. 


4g  PRINCIPLES     OF    DEPRECIATION 

The  book  value  of  the  plant,  i.e.,  the  figure  representing 
first  cost,  will  therefore  tend  to  increase  over  the  figure 
indicating  investment  to  an  amount  'equal  to  the  normal 
accumulated  reserve  for  depreciation,  which  latter  will 
continue  to  increase  only  so  long  as  annual  depreciation 
exceeds  annual  cost  of  replacement.  After  depreciation 
and  actual  replacement  cost  become  equal,  the  plant  is 
normal,  and  the  depreciation  reserve  will  tend  to  gravitate 
about  a  figure  representing  the  ordinary  amount  to  which 
depreciation  may  be  allowed  to  progress  without  suffi- 
ciently impairing  the  plant's  efficiency  to  make  it  more 
profitable  to  increase  the  replacements. 

It  may  be  unnecessary  to  add  that  the  annual  depre- 
ciation charge  is  found  by  totaling  the  sums  deducted  for 
depreciation  for  the  year  in  the  plant  ledger. 

The  Depreciation  Fund 

If  an  actual  depreciation  fund  is  created,  as  suggested 
in  Chapter  IV,  it  would  in  itself  indicate  the  amount  of 
money  to  be  expended  on  replacements  in  order  to  keep 
plant  values  up  to  100%  of  the  original  investment,  and 
as  a  result  would  tend  to  disappear,  remaining  equal  to 
the  depreciation  reserve  only  in  case  all  replacements  made 
are  actual  replacements  of  property  scrapped,  and  have 
the  same  cost  as  the  property  so  scrapped.  The  other 
valid  use  of  the  fund  would  be  the  amortization  of  a  per- 
centage of  the  capital,  thus  permanently  reducing  the 
investment. 


CHAPTER    IV 

DEPRECIATION    RESERVES    VS. 
DEPRECIATION   FUNDS 

The  subject  of  reserves  and  funds  occasions  much  mis- 
understanding. An  examination  of  present-day  practice 
shows  no  unanimity  of  opinion  upon  the  use  of  these  two 
words.  Not  only  are  they  employed  loosely,  but  inter- 
changeably. Some  writers  have  shown  their  true  mean- 
ing, but  in  practice  little  uniformity  exists.  A  variety 
of  conditions  makes  the  employment  of  reserves  bene- 
ficial; this  also  applies  to  funds.  Bad  debts,  contin- 
gencies, accommodation  paper,  bonded  indebtedness,  de- 
preciation, etc.,  admit  of  their  useful  application. 

Purpose  of  Depreciation  Charges 

The  manipulation  of  depreciation  on  the  books  is  quite 
apart  from  the  study  of  the  principles  that  govern  its 
amount  and  the  method  of  determining  it.  Depreciation 
charges  are  adjustments  made  at  the  end  of  a  period  to 
remedy  discrepancies  between  book  accounts  and  the 
things  whose  values  they  indicate.  Such  discrepancies  are 
sometimes  in  approximate  proportion  to  time  expired; 
but  again  they  bear  no  relation  to  time.  An  instance  of 
the  former  is  depreciation  of  houses  from  weathering;1 
of  the  latter,  destruction  by  wind  or  fire.  Between  such 
extremes  are  other  forms  of  deterioration,  the  extent  of 
which  is  more  or  less  directly  proportionate  to  time.  The 
amount  of  the  depreciation  having  been  determined,  the 

1  Amortization,  as  applied  to  bonds,  is  a  perfect  example  of  values  varying 
with  passage  of  time. 

49 


50  PRINCIPLES    OF    DEPRECIATION 

accounts  must  indicate  it  and  make  provision  for  future 
replacement  costs. 

The  nature  of  the  asset  usually  indicates  the  manner  in 
which  it  will  depreciate,  and  perhaps  suggests  the  best 
method  of  determining  its  amount.  But  this  has  been 
touched  upon  in  another  chapter.  Let  us  now  consider 
how  to  indicate  these  changes  on  the  books  and  to  fore- 
stall their  effects. 

Twofold  Object  in  View 

Two  different  things  should  be  done,  viz.:  (1)  write 
down  book  values  to  actual  values,2  carrying  the  amount 
written  off  to  the  Profit  and  Loss  account,  and  (2)  provide 
funds  to  replace  the  assets  when  worn  out.  Failure  to 
distinguish  carefully  between  these  two  procedures  leads 
to  much  confusion.  It  is  an  axiom  that  capital,  and 
therefore  assets,  must  not  be  impaired,  or  the  prosperity 
and  even  the  existence  of  an  enterprise  will  thereby  be 
endangered.  Corporations  have  their  existence  by  the 
sanction  of  the  State,  and  the  preservation  of  their  capital 
is  obligatory;  otherwise  it  is  voluntary.  In  any  event 
deterioration  of  the  value  of  ordinary  assets  is  to  be  de- 
plored. Preservation  of  assets  is  not  accomplished  by 
the  omission  of  the  depreciation  charge.  Apparent  preser- 
vation may  be  accomplished  for  a  certain  length  of  time, 
but  this  is  in  appearance  only  and  evil  will  inevitably  result 
sooner  or  later. 

As  noted,  funds  for  future  replacements  must  be  pro- 
vided. These  should  come  out  of  the  legitimate  income  of 
the  business.  The  depreciation  reserve  indicates  the  sum 
that  will  be  necessary  to  make  such  replacements,  prevents 
its  distribution  as  profits,  but  does  not  set  it  apart  and 

2  This,  of  course,  may  be  done  without  crediting  the  asset  account,  by  deduc- 
tion of  a  "reserve"  account  from  the  asset  account. 


DEPRECIATION     RESERVES    VS.    FUNDS 


label  it  for  that  specific  purpose.  This  is  accomplished  by 
the  establishment  of  a  depreciation  fund,  requiring  an 
entry,  or  entries,  entirely  distinct  from  the  depreciation 
charge. 

Reserves  and  Funds  Distinguished 

While  the  depreciation  reserve  tends  to  preserve  assets 
by  reducing  apparent  net  profits  to  actual  net  profits,  and 
so  avoids  distribution  of  capital  as  profits,  future  replace- 
ments will  have  to  be  made  out  of  the  general  funds  of 
the  treasury.  But  there  is  no  guarantee,  other  than  the 
general  policy  of  the  management,  that  these  will  be 
sufficient.  On  the  other  hand,  a  fund  designated  on  the 
books  for  a  definite  object,  though  not  inviolate,  does 
possess  at  least  a  partial  guarantee  that  it  will  be  so  em- 
ployed. To  illustrate,  Corporation  X,  owning  a  factory 
building  costing  $50,000  and  having  an  estimated  lifetime 
of  thirty  years,  forms  a  depreciation  reserve  each  year, 
crediting  an  account  entitled  "Reserve  for  Depreciation  of 
Factory  Building"  and  charging  Profit  and  Loss.  In 
the  balance  sheet  of  X  this  is  shown  either  as  a  liability, 
thus: 

BALANCE  SHEET  OF  COMPANY  X,  AS  AT.  .... . 


Factory  Building $50,000 

Other  Assets 53,000 


$103,000 


Capital $100,000 

Reserve   for   Depreciation 

of  Factory  Building 1,000 

Dividends   Payable 2,000 


$103,003 


or,  preferably,  as  a  deduction  from  the  corresponding 
asset,  as  it  appears  in  the  first  balance  sheet  on  the  following 
page. 


52  PRINCIPLES     OF    DEPRECIATION 

BALANCE  SHEET  OF  COMPANY  X,  AS  AT. 


Factory  Building.. $50,000 
Less   Reserve    for 
Depreciation....     1,000    $49,000 


Other  Assets 53,000 


$102,000 


Capital $100,000 

Dividends   Payable. ......       2,000 


This  prevents  impingement  upon  capital,  by  limitation 
of  distributable  funds  as  profits.  Had  no  charge  to  de- 
preciation been  made,  the  balance  sheet  would  have  been: 

BALANCE  SHEET  OF  COMPANY  X,  AS  AT 


Factory  Building $50,000 

Other  Assets 53,000 

$103,000 


Capital $100,000 

Dividends  Payable 3,000 


$103,000 


and  after  payment  of  dividends: 

BALANCE  SHEET  OF  COMPANY  X,  AS  AT, 


Factory  Building $50,000 

Other  Assets 50,000 


$100,000 


Capital $100,000 


$100,000 


leaving  assets  overvalued  by  $1,000. 

The  retention  of  sufficient  funds,  by  means  of  the  de- 
preciation reserve,  is  the  essential  step.  If  these  are  per- 
mitted to  remain  a  part  of  the  general  funds  of  the  busi- 
ness, they  are  naturally  reinvested  and  give  rise  to  no 
further  consideration. 

The   problem   of  interest   will  not  arise.      But  if  we 


DEPRECIATION     RESERVES    VS.    FUNDS 


53 


determine  to  earmark   such  funds  and  set   them  apart, 
further  consideration  is  necessary. 

Sinking  Funds 

Sinking  funds  bear  a  sufficiently  close  analogy  to  de- 
preciation funds  to  make  their  consideration  here  valuable 
to  illustrate  principles.  Provision  is  made  in  trust  deeds 
for  the  creation  of  sinking  funds  to  liquidate  bonded  in- 
debtedness, by  requiring  specified  amounts  to  be  paid  into 
the  hands  of  a  trustee  at  designated  intervals.  These  in- 
stalments are  permitted  to  accumulate  at  compound  in- 
terest to  pay  the  obligations,  the  liquidation  of  which  is 
the  purpose  of  the  fund. 

Depreciation  Funds 

Funds  created  for  the  replacement  of  buildings,  ma- 
chinery, etc.,  are  not,  it  is  true,  controlled  by  contract 
obligations;  consequently  the  management  retains  full 
power  over  them.  Otherwise  they  do  not  differ  from 
sinking  funds.  The  same  formulas  that  are  employed  to 
compute  payments  to  a  sinking  fund  may  be  applied  to 
depreciation  funds.  Interest  may  be  handled  differently 
in  the  two  cases  as  a  matter  of  policy.  If  securities  of 
other  corporations  are  purchased  for  the  depreciation 
fund,  it  may  be  more  convenient  to  mingle  the  revenue  de- 
rived therefrom  with  the  general  income  of  the  business, 
instead  of  adding  it  to  the  fund.  The  reason  for  this  is 
that  sinking  fund  trustees  make  a  specialty  of  investments 
and  can  readily  handle  interest  falling  due,  thus  avoiding 
an  excessive  unproductive  cash  balance  in  the  trust  fund. 
Industrial  corporations  cannot  look  after  matters  of 
detail  not  a  part  of  their  own  business.  Therefore  income 
from  funds  in  their  control  can  be  employed  more  pro- 
ductively in  the  business,  and  will  more  than  compensate 


54 


PRINCIPLES     OF    DEPRECIATION 


for  larger  payments  to  the  funds  made  necessary  when 
interest  is  not  added  to  it. 

Formation  of  the  Reserve 

In  later  chapters  the  writer  has  discussed  several 
formulas  for  finding  the  sums  that  must  be  set  aside  to 
accumulate  in  a  given  time  to  a  given  amount.  For  con- 
venience, two  of  these  formulas  are  reproduced  here.  If 
equal  instalments  are  allowed  to  accumulate  at  compound 
interest,  as  in  a  sinking  fund,  then  let  x  represent  the 
amount  of  each  instalment,  v  the  amount  to  which  the 
fund  is  to  accumulate,  r  the  rate  of  interest  plus  1,  and 
n  the  number  of  years  to  run;  then, 


Logarithms  may  be  employed  to  solve  this  formula  if 
the  term  of  years  is  large,  say  more  than  twelve,  because 
of  the  difficulty  of  raising  r  to  the  ;zth  power  by  multipli- 
cation. But  if  interest  is  not  added  to  the  principal,  the 
amount  of  each  instalment  is  determined  thus: 

(2)  x 


n 

v  being  the  sum  accumulated  after  n  years  by  paying  equal 
instalments,  x,  into  the  fund. 

Taking  the  simpler  case  first,  if  Corporation  Y  wishes  to 
establish  a  replacement  fund  for,  say,  a  building  costing 
$25,000,  with  an  estimated  life  of  twenty-five  years,  by 
application  of  formula  (2),  we  find  the  amount  of  each  in- 
stalment to  be  $1,000,  thus: 

25,000 
*  =  _L  1,000 


DEPRECIATION    RESERVES    VS.    FUNDS 


55 


Assuming  that  each  year's  depreciation  amounts  to 
$1,000,  this  is  brought  into  the  books  by  the  following 
entry: 

Profit  and  Loss $1,000.00 

To  Reserve  for  Depreciation  of  Building $1,000.00 

Formation  of  the  Fund 

Next,  having  decided  to  establish  a  depreciation  fund 
for  replacement  of  the  building,  and  having  found  a  suit- 
able manner  in  which  to  invest  the  $1,000,  the  following 
entry  is  made: 

Depreciation  Fund  for  Building $1,000.00 

To  Cash $1,000.00 

For  investment  in,  etc. 

The  balance  sheet  will  then  appear  thus : 

BALANCE  SHEET  OF  COMPANY  Y,  AS  AT 

Building $25,000      Capital $50,000 

Other  Assets 25,000  Reserve    for   Depreciation 

Depreciation    F  u  ri  d    for  of  Building 1,000 

Building   1,000 

$51,000  $51,000 

or,  better  still: 

BALANCE  SHEET  OF  COMPANY  Y,  AS  AT 

Building $25,000       Capital $50,000 

Less  Depreciation  Reserve      1,000 

$24,000 

Other  Assets 25,000 

Depreciation    Fund    for 
Building   .'. 1,000 


$50,000 


$50,000 


PRINCIPLES     OF    DEPRECIATION 


If  no  depreciation  fund  is  established,  the  balance  sheet 
will  be: 

BALANCE  SHEET  OF  COMPANY  Y,  AS  AT.  . 


Building $25,000 

Less  Reserve   for  Depre- 
ciation         1,000 


$24,000 
Other  Assets 26,000 


$50,000 


Capital  .. 


$50,000 


$50,000 


At  the  expiration  of  twenty-five  years  the  depreciation 
reserve,  having  grown  to  the  amount  of  the  original 
building  account,  this  account  will  vanish  from  the  bal- 
ance sheet,  and  the  replacement  will  be  made  thus: 


Cash $25,000.00 


To  Depreciation  Fund  for  Building 

For  sale  of  investment  in,  etc. 

Building  ..  25,000.00 


To  Cash 

For  construction  of  new  building. 


$25,000.00 


25,000.00 


Of  course,  in  practice  such  simplicity  is  impossible,  but 
the  principles  apply,  subject  to  adjustments  for  residual 
values,  variation  from  expected  lifetime  of  assets,  etc. 

If  the  sinking  fund  method  of  adding  interest  to  prin- 
cipal is  followed,  the  computations  are  a  little  more  com- 
plicated. Suppose  Corporation  Y  possesses  a  machine 
costing  $100,000,  with  an  estimated  lifetime  of  ten  years. 
A  replacement  fund  is  to  be  established,  to  accumulate  at 
compound  interest,  4%  being  the  assumed  rate.  Apply- 
ing formula  (1) — shown  on  page  54 — each  annual  instal- 
ment may  be  found  as  follows : 


DEPRECIATION     RESERVES     VS.     FUNDS  57 

x  =  $100,000  X  /Q^oTl1-!  =  $8,329.09 

which  is  transferred  to  the  depreciation  fund  by  the  same 
procedure  as  in  the  previous  case.  As  interest  is  received 
on  the  investments  in  the  depreciation  fund,  it  is  in  turn 
invested  in  some  suitable  way,  as  follows: 


Cash  

To  Reserve  for  Depreciation. 


Depreciation  Fund  for  Machine. 
To   Cash.. 


Terminology 

The  terminology  employed  may  be  altered  from  that 
used  in  the  foregoing  explanation  without  changing  the 
principle  involved.  Thus  in  railroad  accounting  the  de- 
preciation reserve  is  technically  known  as  the  "Reserve 
for  Accrued  Depreciation";  and  in  the  balance  sheet  it  is 
deducted  from  "Road  and  Equipment." 

Advisability  of  Greating  Funds 

Of  course  it  may  not  always  be  desirable  to  accumulate 
definitely  tabulated  sinking  funds  for  replacements,  and 
the  presentation  here  is  rather  for  the  purpose  of  illustrat- 
ing principles  than  of  indicating  the  method  to  be  pur- 
sued in  any  particular  instance.  The  Interstate  Commerce 
Commission  definitely  rejects  this  plan  for  purposes  of 
railroad  accounting,  although  it  states  that  it  is  useful 
under  other  conditions.  The  character  of  the  industrial 
plant  must,  to  a  large  extent,  determine  the  mode  of 
financing  renewals  and  replacements.  There  is  good 
authority  for  the  establishment  of  actual  depreciation 
funds  under  proper  conditions.3  When  making  extensions 


3  See    Proceedings,    National    Electric   Light    Association,   June,    1909,    Vol.    3, 
,page  169. 


cjg  PRINCIPLES     OF    DEPRECIATION 

to  property,  there  would  be  no  objection  to  borrowing 
money  temporarily  from  the  depreciation  fund.  But  this 
borrowed  money  should  be  returned  to  the  fund  as  soon 
as  the  money  intended  for  the  extension  is  secured  through 
the  sale  of  securities  or  otherwise. 

A  Study  of  Balance  Sheets 

A  study  of  twenty-two  balance  sheets  given  in  recent 
reports  of  large  American  corporations  shows  great  lack 
of  uniformity  in  the  management  of  reserves  and  funds.  A 
fair  proportion  of  these  concerns  show  reserves  either  as 
liabilities  or  as  deductions  from  assets.  Few  indicate 
special  funds,  except  sinking  funds  for  the  redemption  of 
bonded  indebtedness.  The  United  States  Steel  Corpora- 
tion balance  sheet  has  an  account  on  the  asset  side  entitled 
"Sinking  and  Reserve  Fund  Assets."  The  Philadelphia 
Rapid  Transit  Company  balance  sheet  shows  "Reserve 
Fund  for  Renewals"  on  the  asset  side,  and  on  the  liability 
side,  of  equal  amount,  "Renewal  Reserve."  The  balance 
sheet  of  the  Third  Avenue  Railway  Company  has  an  ac- 
count on  the  asset  side  entitled  "Deposit  for  Deprecia- 
tion, Renewals,  and  Contingencies,"  and  on  the  liability 
side,  "Reserve  for  Depreciation,  Renewals,  and  Contingen- 
cies." The  Pittsburgh  Brewing  Company  has  a  "Plant 
Sinking  Fund"  among  the  assets. 

Sinking  funds  receive  equally  diversified  names.  The 
International  Paper  Company  has  "Sinking  Fund  Ac- 
counts"; the  United  Gas  Improvement  Company,  "Sink- 
ing Fund  Securities";  the  Interborough  Rapid  Transit 
Company,  "Sinking  Fund  on  5%,  45- Year  Gold  Mort- 
gage Bonds";  and  the  Bethlehem  Steel  Corporation, 
"Special  Funds  in  Hands  of  Trustees  for  Redemption  of 
Mortgages." 

The  following  companies  indicate  the  depreciation  re- 


DEPRECIATION     RESERVES     VS.     FUNDS  59 

serve  on  the  right-hand  side:  Philadelphia  Rapid  Transit 
Company,  Third  Avenue  Railway  Company,  Tennessee 
Copper  Company,  Interborough  Rapid  Transit  Company, 
and  Bethlehem  Steel  Corporation. 

Sears,  Roebuck  &  Co.  and  the  Lehigh  Valley  Railroad 
Company  show  the  reserve  as  a  deduction  from  the  assets. 
The  report  of  Wells,  Fargo  &  Co.  as  of  June  30,  1912, 
indicates  "Reserve  for  Accrued  Depreciation"  deducted 
from  property  and  equipment  account,  whereas  the  report 
for  the  preceding  year  lists  it  on  the  liability  side — an 
indication  of  progress. 

The  Utah  Copper  Company  balance  sheet  shows  an 
account  on  the  liability  side  entitled  "Appropriated  Sur- 
plus— Sinking  Fund";  while  the  balance  sheets  of  Wm. 
Cramp  &  Sons,  the  Baldwin  Locomotive  Works,  the  In- 
ternational Harvester  Company,  the  General  Electric 
Company,  the  American  Tobacco  Company,  and  the 
Amalgamated  Copper  Company,  indicate  neither  reserves 
nor  funds  of  any  kind. 

These  facts  indicate  a  lack  of  uniformity,  justifiable, 
perhaps,  to  a  certain  extent.  Clearness  in  the  balance 
sheet  is,  as  a  rule,  aimed  at;  but  in  some  cases  it  is  difficult 
to  believe  that  such  is  the  intention.  The  balance  sheet 
ought  to  reflect,  not  obscure,  conditions.  The  proper 
tabulation  therein  of  the  depreciation  reserves  and  funds 
is  of  much  assistance  to  a  clear  and  consistent  presentation 
of  facts. 


CHAPTER    V 

DEPRECIATION  AND  EFFICIENCY 

Relation  of  Depreciation  to  Efficiency 

Every  plant  must  be  maintained  at  a  certain  degree  of 
efficiency,  to  enable  it  to  meet  the  various  demands  made 
upon  it  for  service.  In  some  cases,  such  as  the  telephone 
business,  the  general  efficiency  must  be  kept  very  high, 
otherwise  dissatisfaction  with  the  service  soon  appears. 
While  a  close  connection  exists  between  efficiency  and  de- 
preciation, a  distinction  must  at  the  same  time  be  recog- 
nized. Of  course,  a  loss  of  efficiency  in  a  unit  of  plant  must 
in  time  inevitably  occur  as  the  result  of  depreciation.  But 
loss  of  efficiency  of  the  whole  plant  does  not  occur  in  any 
degree  proportionate  to  loss  by  depreciation.  In  fact,  com- 
posite depreciation  of  plant  may  give  rise  to  little  or  no 
loss  of  efficiency. 

The  failure  to  distinguish  between  depreciation  and 
efficiency  may  account  for  the  failure  of  many  manage- 
ments to  make  due  allowance  for  depreciation.  Oftentimes 
it  is  said  that  this  or  that  machine  is  as  good  as  new,  after 
being  used,  say,  ten  or  fifteen  years;  and  as  the  time  of  dis- 
card seems  indefinite,  nothing  is  written  off.  It  is  true  that 
the  element  of  uncertainty  is  always  present  even  in  the 
most  careful  attempts  to  make  depreciation  allowances.  But 
much  of  the  confusion  arises  from  a  failure  to  recognize  the 
essential  difference  between  loss  of  efficiency  and  loss  of 
capital  assets  through  depreciation. 

City  of  Beloit  vs.  Beloit  Water,  Gas  and  Electric  Company 

Buildings,  machines,  tools,  etc.,  remain  in  unimpaired 
efficiency  for  years.  But  sooner  or  later  they  must  wear 

60 


DEPRECIATION     AND     EFFICIENCY  6l 

out  or  become  obsolete  or  inadequate.  In  this  connection, 
the  statement  of  the  Wisconsin  Railroad  Commission  in 
City  of  Beloit  v.  Beloit  Water,  Gas  and  Electric  Company1 
is  of  interest,  being  to  the  effect  that  erroneous  ideas  of  the 
value  of  -property  that  has  been  in  use  for  some  time  with- 
out requiring  extensive  repairs,  are  apt  to  be  formed;  but 
that  the  time  always  comes  when  a  casual  observation  can 
detect  the  loss  of  value. 

Efficiency  Defined 

Depreciation  and  efficiency  must  be  carefully  distin- 
guished, the  difficulty  being  due  partly  to  a  confusion  or 
misunderstanding  of  the  terms. 

Efficiency  is  a  word  of  frequent  occurrence  in  modern 
business  parlance.  It  applies  both  to  labor  and  to  machin- 
ery. As  to  machinery  it  raises  questions  of  construction, 
adequacy,  suitability,  and  general  usefulness.  It  is  the 
practical  test  of  present  effectiveness,  to  which  most  other 
considerations  are  subordinate.  Beauty  of  architecture  in 
buildings  and  gracefulness  of  construction  in  machines  are 
desirable,  but  under  competitive  conditions  such  considera- 
tions give  way  to  the  all-important  question  of  efficiency. 
Efficiency  is  prized  and  sought  after ;  inefficiency  is  shunned 
and  despised.  In  men,  efficiency  consists  in  highly  special- 
ized or  broadly  developed  faculties;  in  machines,  in 
powerful  construction  or  delicately  adapted  mechanisms. 
Its  possession  is  always  coveted,  and  its  loss  always  re- 
gretted. 

The  Factors  of  Value 

But  efficiency,  the  test  of  present  usefulness,  is  not  the 
only  factor  that  determines  value.  Value  depends  upon 
present  usefulness,  it  is  true,  but  it  also  depends  upon  the 

>7  W.  R.  C.  R.   187,  235,  decided  July  19,  1911. 


62  PRINCIPLES    OF    DEPRECIATION 

length  of  time  over  which  such  usefulness  will  continue. 
Two  similar  machines  may  be  equally  efficient  today ;  but 
one  may  continue  to  be  useful  for  two  years  and  the  other 
for  four.  Can  we  say  that  they  have  equal  value?  There 
may  be  some  uncertainty  in  individual  cases ;  but  the  uncer- 
tainty is  limited  within  certain  bounds,  and  to  a  great 
degree  vanishes  when  averages  are  considered,  just  as  the 
uncertainties  of  lifetime  vanish  when  large  numbers  of  lives 
are  considered.  The  lifetime  of  a  single  freight  car  is  very 
uncertain,  but  the  average  lifetime  of  a  thousand  cars  is 
ascertainable  to  the  fraction  of  a  year. 

Depreciation — What  It  Is 

The  significance  of  the  words  depreciation  and  efficiency 
cannot  be  too  clearly  grasped.  Depreciation  is  necessarily  a 
somewhat  theoretical  and  uncertain  quantity.  Broadly 
ppeaking,  it  includes  wear  and  tear,  obsolescence,  and  inade- 
quacy. It  may  not  be  possible  to  give  an  all-inclusive  defini- 
tion of  depreciation;  rather  its  significance  in  each  concrete 
case  ought  to  be  carefully  studied.  The  Interstate  Com- 
merce Commission,  the  New  York  Public  Service  Commis- 
sion, and  similar  bodies  do  not  say  just  what  and  how  much 
must  be  included  in  the  depreciation  charge,  but  leave  this 
largely  to  the  individual  corporations  to  determine. 

Individual  peculiarities  and  customs  will  have  their 
v,  eight  in  determining  the  depreciation  charge.  Thus,  if 
repairs  are  adequately  met  out  of  revenue,  the  annual  pro- 
vision for  depreciation  may  be  materially  smaller  than  if 
they  are  neglected,  owing  to  the  greater  longevity  of  prop- 
erty adequately  repaired. 

Comparison  of  Depreciation  and  Efficiency 

Form  4  represents  the  character  of  depreciation  figured 
on  a  straight  line  basis,  also  of  efficiency,  both  curves  apply- 


DEPRECIATION    AND     EFFICIENCY  63 

ing  to  the  same  unit  of  plant.  If  the  distance  from  o  to  x 
represents  the  efficiency  of  a  new  machine,  or  100%,  and 
the  distance  from  o  to  3;  represents  the  lifetime  of  the  same 
machine,  say,  ten  years,  then  the  straight  line  xy  represents 
the  progress  of  the  theoretical  straight  line  depreciation, 
while  the  curved  line  xcy  indicates  the  rapidity  with  which 
efficiency  declines. 


Time 


Form  4.     Curves  Showing  Progress  of  Uniform  Depreciation 
and  of  Diminishing  Efficiency 

From  this  diagram  it  will  be  seen  that,  whereas  the  effi- 
ciency of  the  machine  continues  almost  unimpaired  until 
the  tenth  year,  the  theoretical  straight  line  depreciation  re- 
duces the  value  of  the  machine  by  an  equal  amount,  nearly 
10%,  -each  year.  Objection  may  be  made  on  the  ground 
that  this  straight  line  does  not  represent  actual  deprecia- 
tion, and  that  should  a  sale  occur  at  the  end  of  the  fifth  or 
sixth  year  the  machine  would  very  likely  bring  considerably 
more  or  less  than  50%  of  cost.  Although  this  is  true, 
it  should  be  remembered  that  depreciation  is  usually 


64  PRINCIPLES    OF    DEPRECIATION 

figured  with  reference  to  future  replacement,  not  future 
sale. 

From  this  standpoint  it  does  not  ordinarily  matter 
greatly  if  theoretical  and  actual  depreciation  do  differ  con- 
siderably at  times  during  the  life  of  a  unit.  Actual  depre- 
ciation is  always  somewhat  indeterminate,  yet  it  is  a  con- 
sideration of  vital  importance  in  valuation  work. 

In  place  of  the  straight  line  to  represent  depreciation, 
one  of  the  more  complicated  curves  may  be  adopted,  but  in 
no  case  would  such  a  curve  correspond  even  approximately 
with  the  line  indicating  decrease  of  efficiency.  Deprecia- 
tion is  determined,  theoretically,  by  the  method  of  compu- 
tation adopted ;  and  while  it  is  desirable  to  have  this  corre- 
spond as  nearly  as  possible  to  actual  depreciation,  it  is  un- 
certain, except  after  investigation,  which  method  most 
closely  approximates  this  result.  While  it  may  be  desirable 
to  accumulate  a  reserve  whose  growth  exactly  counter- 
balances the  gradually  decreasing  value  of  the  asset,  it  is 
perhaps  more  important  that  it  shall  be  sufficient  to  make 
the  necessary  replacements  when  desired. 

Investment  to  be  Preserved 

From  what  has  been  said  it  is  apparent  that  while  in 
the  long  run  efficiency  is  dependent  upon  the  extent  to 
which  depreciation  has  occurred,  it  may  for  a  long  time 
remain  quite  independent  of  accruing  depreciation.  High 
present  efficiency  ought  not,  therefore,  to  be  used  as  an 
excuse  for  failing  to  make  adequate  provision  for  depre- 
ciation. Such  a  short-sighted  policy  can  only  lead  to  diffi- 
culties later  on.  Not  merely  efficiency  must  be  retained, 
but  the  investment  as  well,  and  for  the  continued  prosperity 
of  the  concern  one  is  as  necessary  as  the  other. 

Efficiency  is  the  test  of  present  daily  effectiveness. 
Depreciation  is  the  slow  process  by  which  industrial  plants 


DEPRECIATION.  AND     EFFICIENCY  £5 

whatever  its  present  effectiveness  may  be,   gradually  ap- 
proaches the  time  of  discard  and  replacement. 

Efficiency  Not  to  be  Impaired 

In  case  of  extensive  plants,  as  water  works,  electric  rail- 
ways, and  so  on,  a  composite  condition  results  from  the 
existence  of  a  large  number  of  units  of  plant  of  different 
kinds  in  various  stages  of  depreciation.  Constant  repairs 
and  replacements  prevent  the  plant  as  a  whole  from  drop- 
ping in  value  below  a  certain  percentage  of  cost  new,  or 
cost  of  reproduction.  If  we  assume  that  normal  depre- 
ciated plant  value  is  80%  of  reproduction  cost,  it  is  evident 
that  the  original  investment  has  depreciated  20%  in  spite 
of  renewals.  But  efficiency  should  remain  at  100%  as  long 
as  all  necessary  repairs  and  replacements  are  made ;  and  the 
producing  power  of  the  plant  should  be  increased  if,  instead 
of  amortizing  capital,  replacement  of  values  lost  through 
composite  depreciation  is  made  by  the  purchase  of  addi- 
tional plant. 

There  are  other  reasons  why  an  old  plant  should  possess 
a  larger  earning  power  than  a  new  one,  such  as  adapta- 
bility and  smoothness  of  operation.  These  are  also  addi- 
tional reasons  for  distinguishing  between  efficiency  and 
depreciation. 


Part  II — Practical  Applications 


CHAPTER    VI 

REGULATION  BY  COURTS  AND  COMMISSIONS 

The  State's  Relation  to  Industry 

It  is  in  accord  with  our  present  theory  of  government 
for  the  State  to  undertake  in  an  increasing  degree  the 
regulation  of  industries.  This  is  for  the  prevention  of  evils 
and  the  guarantee  of  good  service  to  the  public.  This  ten- 
dency assumes  'many  and  varied  forms  as  it  develops  and 
extends  into  new  fields.  It  has  arisen  because  of  the  failure 
of  competition  to  secure  good  service  and  proper  treatment 
for  all.  In  some  cases  the  transactions  of  corporations  are 
regulated  with  extreme  minuteness,  from  general  principles 
of  policy  to  the  details  of  daily  routine. 

The  Importance  of  Accounts 

An  essential  feature  of  any  extensive  business  under- 
taking is  its  system  of  accounts.  It  concerns  both  the  pro- 
prietorship and  the  public,  frequently  determining  a  policy 
that  may  benefit  or  injure  the  one  or  the  other.  It  is  not 
surprising,  therefore,  that  accounting  systems,  methods, 
and  theories  have  become  the  subject  of  legislative  and 
judicial  attention.  With  the  rapid  growth  of  corporate 
enterprise  and  the  readiness  with  which  large  numbers  of 
persons  become  co-sharers  in  the  capital  stock  of  big  con- 
cerns, however  small  their  respective  holdings,  there  arises 
the  problem  of  safeguarding  their  interests.  When,  owing 
to  absence,  ignorance,  or  other  cause,  they  have  no  voice  in 
the  management  of  the  enterprise  which  they  promote  by 

66 


COURT    AND     COMMISSION    REGULATION  67 

.  their  investments  and  to  which  they  look  for  an  increase  in, 
or  at  least  the  preservation  of,  their  wealth,  they  demand  a 
certain  amount  of  protection  from  the  State. 

The  stockholder  is  chiefly  interested  in  two  things — 
the  preservation  of  his  capital,  and  the  income  derived  from 
it.  He  reads  his  company's  annual  report,  trusting  that  the 
facts  are  as  indicated  in  the  balance  sheet  and  the  profit 
and  loss  statement.  If  they  are  not,  he  has  neither  the 
assurance  that  his  dividend  is  the  real  amount  of  his  income 
nor  that  his  capital  is  unimpaired.  If  all  proper  charges 
have  been  made  against  gross  profits  for  the  fiscal  period, 
his  dividends  represent  true  profit.  If  not,  profits  are  over- 
stated and  capital  is  decreased  to  the  extent  of  the  error. 

Meaning  of  "Net  Profits" 

Practically  all  the  states  have  enacted  laws  to  the  effect 
that  dividends  must  be  paid  only  from  net  profits ;  but  there 
is  some  question  as  to  the  significance  of  the  phrase  "net 
profits,"  and  a  lengthy  combat  has  resulted  over  the  ques- 
tion of  the  inclusion  of  an  annual  depreciation  charge 
among  the  more  obvious  expenses.  Yet,  of  all  expenses, 
this  is  perhaps  the  least  avoidable,  and  net  profits  do  not 
exist  until  proper  allowance  has  been  made  for  it. 

There  is  little  disagreement  in  framing  a  definition  of 
net  profits  in  general  terms,  but  trouble  arises  when  we  try 
to  discover  the  detailed  deductions  that  must  be  made  from 
gross  profits  to  arrive  at  net  profits.  Thus  an  English  court 
declares,  net  profits  to  be  the  excess  of  current  gains  over 
the  working  expenses,  as  indicated  by  the  revenue  accounts  ;* 
and  a  New  Jersey  court  says  that  net  profit  is  the  clear  gain 
of  a  business  venture  shown  after  deducting  the  invested 
capital,  the  expenses  of  operation,  and  losses  sustained.2 

'/n  re  London,  etc.,  Bank,  72  L.  T.  227;  aff'd  (1885),  2  Ch.  166. 
2  Park  v.  Grant  Locomotive  Works,  40  N.  J.  Eq.  144;  3  Atl.  162. 


68  PRINCIPLES    OF    DEPRECIATION 

Division  of  opinion  over  these  statements  first  occurs  when 
we  attempt  to  detail  the  actual  working  expenses,  expenses 
of  operation,  and  losses  sustained. 

The  meaning  of  these  definitions  is  that  capital  must  not 
be  impaired  by  declaring  dividends  out  of  it  under  the  guise 
of  profits.  To  say  that  capital  must  not  be  parceled  out  as 
dividends  and  that  dividends  must  be  declared  out  of  net 
profits,  is  merely  viewing  the  matter  from  different  points. 
The  former  expression  is  used  when  capital  has  been  delib- 
erately encroached  upon,  as  in  Appleton  v.  American  Malt- 
ing Company,3  where  no  question  existed  as  to  impairment 
of  capital.  The  latter  expression  applies  when  the  bulk  of 
the  dividend  is  proper  but  in  addition  to  its  inclusion  of  net 
profits  it  includes  a  little  capital  also. 

Preservation  of  Capital 

When  capital  is  deliberately  distributed  through  divi- 
dends, there  is  no  ground  for  dispute.  The  courts  are  in 
such  close  accord  as  to  its  illegality  and  the  personal  respon- 
sibility of  the  directors  for  the  amount  of  such  illegal  divi- 
dends authorized,  that  little  need  be  said  about  it.  But 
upon  approaching  the  subject  from  the  other  side,  to  learn 
what  reservations  must  be  made  in  order  to  insure  preserva- 
tion of  the  capital,  the  courts  fail  to  satisfy  us  with  either 
a  clear  or  a  consistent  analysis.  They  point  out  and  punish 
the  gross  offense,  but  they  do  not  show  how  the  evil  results 
which  that  offense  produces  may  be  avoided  when  those 
effects  result  incidentally  through  the  overpayment  of  divi- 
dends and  consequent  injury  to  capital.  Thus,  in  the  case 
of  Belfast  &  M.  L.  R.  Co.  v.  City  of  Belfast,4  the  court 
asserted  that  before  dividends  could  be  declared,  several 
kinds  of  charges  must  be  met.  "Therefore,"  runs  the  de- 

»54  Atl.  Rep.  454  (N.  J.). 
*  1  Atl.  Rep.  362;  77  Me.  445. 


COURT    AND     COMMISSION     REGULATION 


69 


cision,  "if  there  is  a  bonded,  funded,  permanent,  or  standing 
debt,  the  interest  on  it  must  be  reckoned  out  of  net  earnings. 
If  there  is  a  floating  debt  which  it  is  not  wise  or  prudent 
to  place  in  the  form  of  a  funded  debt,  or  to  postpone  for 
later  payment,  that  should  also  be  paid.  If  the  financial 
situation  of  the  company  is  such  as  to  render  it  expedient 
to  commence  or  continue  the  scheme  of  a  sinking  fund  for 
the  extinguishment  of  the  company's  indebtedness  some  day 
or  other,  an  annual  contribution  out  of  the  net  earnings  for 
that  purpose  would  be  reasonable.  These  deductions  made 
from  the  net  earnings,  the  balance  will  be  the  profits  of  the 
company  distributable  among  stockholders." 

Shall  we  say  that  the  corporation,  after  conforming  to 
the  court's  ruling,  stood  in  no  danger  of  impairing  its  capi- 
tal ?  Although  this  was  an  early  case,  yet  not  without  pre- 
cedent,5 the  improvement  since  made — excepting  a  few 
decisions  and  the  work  of  the  Interstate  Commerce  Com- 
mission and  of  certain  state  public  service  commissions — 
has  been  slight. 

Decisions  on  Depreciation 

In  the  earlier  case  (1878)  of  Union  Pacific  R.  R.  v. 
United  States6  the  Supreme  Court  gave  an  admirable  defini- 
tion of  net  profits :  "Theoretically,  the  expenses  chargeable 
to  earnings  include  the  general  expenses  of  keeping  up  the 
organization  of  the  company,  and  all  expenses  incurred  in 
operating  the  works  and  keeping  them  in  good  condition 
and  repair."  This  case  was  a  precedent  for  the  Maine  court 
in  Belfast  &  M.  L.  R.  Co.  v.  City  of  Belfast  cited  above, 
and,  presumably,  shaped  that  decision  to  a  certain  extent. 
But  the  weakness  of  the  decision  is  its  failure  to  define 


5  The  court  quoted  from  the  following  in  substantiation:  Taft  v.  Railroad  Co., 
8  R.  I.  316;  St.  John  v.  Erie  Ry.  Co.,  10  Batchf.  271;  S.  C.,  22  Wall.  136; 
Union  Pacific  R.  R.  v.  U.  S.,  99  U.  S.  402. 

e  99  U.  S.  402. 


70  PRINCIPLES     OF    DEPRECIATION 

accurately  what  expenses  are  necessary  to  keep  a  railroad  in 
good  condition.  Did  the  court  mean  to  include  therein  all 
charges  now  indicated  under  the  three  heads,  repairs,  re- 
newals and  replacements,  or  did  it  refer  to  ordinary  repairs 
only?  The  same  decision  is  marred  by  the  assertion  that  it 
is  often  better  to  charge  betterments  to  revenue  than  to 
capital,  which  in  itself  is  sufficient  to  upset  all  calculations 
as  to  net  profits. 

Depreciation  a  Proper  Charge 

In  the  same  year  that  the  decision  in  Union  Pacific  R.  R. 
v.  United  States  was  given  (1898),  the  Supreme  Court  in 
United  States  v.  Kansas  Pacific  Railway  Company7  indi- 
cated that  it  limited  the  charges  to  gross  profits  to  the  ex- 
penditures actually  incurred,  refusing  to  accept  as  a  proper 
charge  to  profits  a  sum  indicated  as  necessary  to  put  the 
road  in  proper  repair  but  not  actually  expended.  This  case 
draws  a  clean  line  between  current  repairs  on  the  one  hand, 
and  deferred  renewals  and  replacements  on  the  other.  It  is 
difficult  to  understand  how,  under  this  ruling,  a  reserve 
could  be  established  for  replacement,  or  how  any  plan  of 
extending  the  cost  of  extensive  repairs  over  a  series  of 
years  could  be  pursued.  In  the  light  of  recent  decisions  of 
the  Interstate  Commerce  Commission  it  is  easy  to  see  the 
inconsistency  in  the  definition  of  net  profits  given  by  the 
Supreme  Court  and  in  its  attempt  to  apply  it.  In  more  re- 
cent decisions  of  the  Supreme  Court,  notably  City  of  Knox- 
ville  v.  Water  Company8  and  Willcox  v.  Consolidated  Gas 
Company,9  depreciation  is  regarded  as  a  proper  charge.  In 
the  former  case  the  Supreme  Court  says  that  a  company 
"is  not  bound  to  see  its  property  gradually  waste,  without 
making  provisions  out  of  earnings  for  replacement,"  and 

7  99  U.  S.  459. 

8  212  U.  S.  1. 
"212U.  S.  19. 


COURT    AND     COMMISSION    REGULATION  jl 

adds  that  it  is  privileged  to  keep  its  property  unimpaired  by 
the  expenditure  of  earnings,  in  order  that  after  a  period  of 
years  the  original  value  may  be  still  maintained. 

Our  courts  have  done  little  to  compel  a  regular  charge 
to  depreciation.  Less  conspicuous  but  more  effective  have 
been  the  efforts  of  public  accountants — both  in  this  country 
and  in  England — and  also  of  bankers,  to  secure  adequate 
depreciation  charges.  Many  corporations  now  make  regu- 
lar depreciation  charges  in  order  to  secure  an  unqualified 
audit  certificate.  Much  time  has  been  spent  in  clearing 
away  false  conceptions,  and  we  are  entering  upon  a  period 
in  which  what  at  first  appeared  to  be  an  improper  charge, 
and  then  a  legitimate  one,  is  now  regarded  as  a  necessary 
one.  The  movement  has  been  considerably  aided  by  the 
publications  of  the  Interstate  Commerce  Commission, 
which  present  the  results  of  long  experience  on  the  part  of 
railway  accounting  officers  and  public  accountants.  The 
method  of  charging  depreciation  employed  by  the  Commis- 
sion is  the  outcome  of  its  attempt  to  aid  itself  and  others  in 
arriving  at  the  facts  in  railroad  administration. 

How  Depreciation  Charge  is  Regulated 

It  is  unusual  for  the  commissions,  in  their  prescription 
of  uniform  systems  of  accounting,  to  more  than  suggest 
the  amount  or  even  the  method  of  determining  the 
amount  of  the  depreciation  allowance.  It  is  deemed  best 
to  leave  this  to  the  judgment  of  those  most  thoroughly 
acquainted  with  the  conditions  in  each  instance.  Rather 
it  is  the  principle  of  the  accounting  procedure  that  is  en- 
forced, since  this  allows  room  for  variations  in  extent, 
rapidity,  or  character  of  depreciation.  A  brief  description 
of  the  requirements  of  two  leading  commissions  possess- 
ing plenary  powers  over  public  service  companies,  viz., 
the  Interstate  Commerce  Commission  and  the  New  York 


j2  PRINCIPLES     Of     DEPRECIATION 

Public  Service  Commission  for  the  First  District,  in  so  far 
as  they  refer  to  depreciation,  will  serve  to  show  the 
present  tendency. 

Regulations  of  Interstate  Commerce  Commission 

According  to  Act  of  Congress,  the  Interstate  Com- 
merce Commission  is  given  power  to  prescribe  uniform 
accounts  for  gas  and  electric  corporations  in  the  District 
of  Columbia.10  According  to  its  published  classification,11 
the  accounts  are  divided  into  three  fundamental  classes: 
(1)  operating  revenue  and  expense  accounts,  (2)  income 
accounts,  and  (3)  balance  sheet  and  capital  accounts. 
Under  these  come  the  subdivisions,  or  primary  accounts. 
Thus,  for  gas  corporations,  operating  revenue  falls  into 
six  distinct  accounts,  which  are  designated  by  symbolic 
letters  with  annexed  numerals,  as  GlOl,  G102,  and  so  on. 
Operating  expenses  for  gas  corporations  are  divided  into 
five  general  classes:  (1)  production  expenses,  (2)  trans- 
mission and  distribution  expenses,  (3)  street  and  park 
lighting  expenses,  (4)  commercial  expenses,  and,  lastly, 
(5)  general  and  miscellaneous  expenses.  Production  ex- 
penses are  separated  into  seventeen  classes,  four  of  which 
are  maintenance  accounts  for  work  and  station  structures, 
power  plant  equipment,  gas  apparatus,  and  work  tools, 
respectively.  Transmission  and  distribution  expenses  are 
separated  into  nine  classes,  four  of  which  are  maintenance 
accounts  for  gas  mains  and  services,  gas  meters,  distribu- 
tion tools,  and  gas  appliances,  respectively.  Street  and 
park  lighting  expenses  are  separated  into  two  classes,  one 
of  which  is  a  maintenance  account  for  street  lamps.  Gen- 
eral miscellaneous  expenses  are  separated  into  sixteen 
classes,  one  of  which  is  a  maintenance  account  for  general 


10  Effective  January  1,  1910. 

11  Uniform  System  of  Accounts  for  Gas  Corporations  and  Electric  Corporations 
in  the  District  of  Columbia. 


COURT    AND    COMMISSION    REGULATION  73 

structure,  and  a  second  is  an  account  for  general  amortiza- 
tion. A  similar  classification  is  followed  for  electric  cor- 
porations. It  is  in  these  maintenance  accounts  that  the 
depreciation  of  the  different  capital  accounts  is  expressed. 
In  this  connection  it  should  be  noted  that  the  maintenance 
accounts  and  capital  accounts  are  complements  of  each 
other. 

Income  accounts  form  the  next  general  division. 
There  are  seventeen  classes  of  these,  the  account  for 
operating  expenses  being  the  one  in  which  the  deprecia- 
tion costs  or  expenses  as  expressed  in  the  maintenance 
and  depreciation  accounts  are  collected  for  deduction  from 
gross  income. 

The  third  general  division  is  composed  of  the  balance 
sheet  accounts.  These  indicate  assets,  liabilities,  and 
capital.  The  asset  accounts  are  twenty-five  in  number, 
and  the  liability  and  capital  accounts  fourteen  in  number. 
Liability  account  37  is  entitled  "Accrued  Amortization  of 
Capital,"  and  is  complementary  to  operating  expense  ac- 
count G174,  entitled  "General  Amortization."  To  Gen- 
eral Amortization  (G174)  an  amount  is  charged  monthly 
necessary  to  cover  wear  and  tear,  obsolescence,  and  in- 
adequacy accrued  during  the  month  in  the  tangible  capital, 
a  reasonable  amount  for  depreciation  of  intangible  capital, 
and  a  sufficient  amount  to  cover  ordinary  casualties,  less 
the  amounts  charged  for  repairs  in  the  various  main- 
tenance accounts.  The  amount  so  charged  is  in  turn 
credite.d  to  liability  account  37,  "Accrued  Amortization 
of  Capital";  thus: 

General  Amortization  (G174) $.    .    ... 

To  Accrued  Amortization  of  Capital $....-.. 

To  cover  depreciation,  inadequacy,  wear  and 
tear,  loss  of  intangible  values,  and  extraor- 
dinary casualties,  not  covered  in  current 
maintenance  for  the  month  ending 


74 


PRINCIPLES     OF    DEPRECIATION 


Purpose  of  the  Reserve 

It  must  be  remembered  that  the  reserve  for  accruec 
amortization  of  capital  is  what  its  name  implies — an  ac- 
count to  adjust  depreciation  not  made  good  through 
maintenance.  The  need  of  such  provision  was  indicated 
in  Chapter  I,  "Character  of  Industrial  Plant,"  since,  par- 
ticularly during  the  first  ten  or  fifteen  years  of  the  utility's 
life,  depreciation  greatly  exceeds  maintenance  costs.  The 
Interstate  Commerce  Commission  suggests  that  the  cor- 
poration's experience  during  the  preceding  five  years  be 
considered  in  estimating  depreciation.  Permission  is  given 
to  base  the  rate  on  the  amount  of  gas  sold.  Whenever 
any  capital  is  retired  from  service,  the  original  money 
cost,  less  salvage,  is  charged  to  Accrued  Amortization  of 
Capital.  This  is  proper,  since  the  reserve  has  been  ac- 
cumulated to  offset  the  depreciation,  which  amounts  to 
cost  less  salvage.  In  case  of  property  purchased  before 
December  31,  1909,  however,  the  depreciation  applicable 
to  the  period  following  that  date  only,  can  be  charged  to 
Accrued  Amortization  of  Capital.  The  depreciation  ac- 
cruing before  that  date  should  be  charged  to  Profit  and 
Loss,  unless  it  was  actually  covered  by  a  depreciation  re- 
serve. In  the  latter  case  it  would  be  charged  to  such 
reserve  account. 

The  plan  adopted  by  the  New  York  Public  Service 
Commission,  First  District,  differs  only  in  detail  from  the 
above.12 

Railroad  Companies 

Railroad  companies  doing  interstate  business  maintain 
the  following  general  accounts  for  operating  expenses:13 

12  Uniform    System    of    Accounts    of    Street    and    Electric    Railways,    effective 
January   1,   1909.     Also  Uniform  System  of  Accounts  for  Electrical  Corporations, 
effective  January  1,   1909. 

13  Classification  of  Operating  Expenses,  third  revised  issue    (I.  C.  C.). 


COURT    AND     COMMISSION     REGULATION 


75 


1.  Maintenance  of  Way  and  Structures 

2.  Maintenance  of  Equipment 

3.  Traffic  Expenses 

4.  Transportation  Expenses 

5.  General  Expenses 

Under  these  general  accounts  are  grouped  primary  ac- 
counts. Included  under  the  general  account  "Mainte- 
nance of  Equipment,"  for  instance,  are  twenty-nine  primary 
operating  expense  accounts.  Each  subdivision  of  equip- 
ment— steam  locomotives,  passenger-train  cars,  electric 
equipment  of  cars,  etc. — is  given  three  separate  primary 
operating  expense,  or  maintenance,  accounts  for  (1)  re- 
pairs, (2)  renewals,  and  (3)  depreciation. 

Classification  of  Depreciation  Charges 

The  third  revised  issue  of  the  classification  of  operating 
expense  details  the  charges  to  be  made  to  these  accounts. 
Thus,  to  ''Steam  Locomotives — Repairs"  are  charged  cost 
of  material  used,  less  salvage,  and  cost  of  labor  in  repairing 
steam  locomotives  and  tenders  and  their  fixtures.  To 
"Steam  Locomotives — Renewals"  are  charged  original 
cost,  record  value,  or  purchase  price  of  steam  locomotives 
condemned,  destroyed,  or  sold,  less  the  amount  previously 
charged  to  depreciation  to  date  of  retirement  and  the 
scrap  value.  For  "Steam  Locomotives — Depreciation"  a 
monthly  charge  of  a  certain  per  cent  of  the  original 
cost,  record  value,  or  purchase  price,  is  made  for  the 
establishment  of  a  reserve  for  future  replacements.  Steam 
locomotives  are  one  of  the  seven  classes  of  equipment 
upon  which  formal  repair  renewal  and  depreciation 
charges  are  required.  These  are: 

1.  Work  equipment 

2.  Steam  locomotives 


76  PRINCIPLES     OF    DEPRECIATION 

3.  Electric  locomotives 

4.  Passenger-train  cars 

5.  'Freight-train  cars 

6.  Electric  equipment  of  cars 

7.  Floating  equipment 

Before  the  third  revision  of  operating  expenses  became 
effective  on  July  1,  1907,  repairs,  renewals,  and  deprecia- 
tion had  been  grouped  in  one  account,  "Repairs  and  Re- 
newals." The  change  was  made  in  the  interests  of  better 
accounting,  but  in  some  quarters  the  impression  gained 
ground  that  operating  expenses  would  thereby  be  in- 
creased. This,  as  the  Commission  explained,  would  be 
the  case  only  where  property  has  not  been  maintained  in 
the  past.  The  amount  charged  for  depreciation  of  prop- 
erty, as  indicated,  is  credited  to  "Reserve  for  Accrued  De- 
preciation." This  is  a  balance  sheet  account  and  should 
be  deducted  from  the  investment  account  "Road  and 
Equipment"  for  the  purpose  of  showing  actual  work  as 
at  the  date  of  the  balance  sheet.  The  Reserve  for  Accrued 
Depreciation  is  both  an  adjustment  and  a  clearing  ac- 
count. It  is  a  clearing  account  because  when  equipment  is 
retired  its  cost,  less  salvage,  is  charged  to  this  account.14 

This  appears  to  be  an  abandonment  of  the  theory  that 
railroads,  owing  to  their  extensive  and  varied  assets,  can 
with  safety  permit  all  charges  for  repairs,  renewals,  and 
replacements  to  be  made  to  current  revenue  for  the  year 
or  period  in  which  repairs,  renewals,  and  replacements  are 
made.  As  a  matter  of  fact  depreciation  to  a  certain  ex- 
tent, say,  15  or  20%,  will  occur  no  matter  how  varied  or 
extensive  the  equipment.  Such  loss  in  the  investment 
can  be  guarded  against  only  through  depreciation  re- 
serves. It  is  to  be  noted,  however,  that  there  is  a  differ- 


14  Accounting  Series,  Circular  No.   120,  case  567. 


COURT    AND    COMMISSION    REGULATION  77 

ence  in  the  manner  of  handling  such  reservations  under 
the  plan  suggested  by  the  Interstate  Commerce  Commis- 
sion, from  that  sometimes  followed. 

Two  methods  of  handling  depreciation  reserves  are  in 
vogue — the  insurance  method  and  the  sinking  fund 
method.  Under  the  sinking  fund  method  a  certain  per- 
centage of  the  value  of  a  property  is  written  off  each  year 
and  accumulated  by  compound  interest,  the  investments 
usually  being  made  in  outside  securities,  so  that  when  the 
time  for  replacement  arrives  the  fund  will  be  sufficient  to 
purchase  the  property  necessary  to  make  the  replacement. 
This  it  will  do  if  the  cost  of  the  replacement  is  the  same 
as  the  original  value  of  the  property  replaced,  or,  if  greater 
in  value,  with  an  additional  expenditure,  which  will  be,  not 
a  replacement,  but  a  betterment. 

Under  the  insurance  method,  which  is  approved  by  the 
Interstate  Commerce  Commission,  compound  interest  is  not 
used,  and  the  fund  is  not  designated  for  the  replacement  of 
any  specific  part  of  capital;  nor  is  the  fund  accumulated 
through  the  depreciation  charge  reserved  until  it  can  be 
expended  in  replacing  the  identical  property  upon  which 
it  was  figured.  Rather  it  is  spent  wholly  or  partly  during 
the  same  year  in  which  it  is  charged,  by  replacing  other 
equipment  or  purchasing  additional  equipment.  Of 
course,  the  entire  accumulation  need  not  be  spent  during 
the  year  in  which  it  is  accumulated.  Business  policy  must 
determine  whether  replacements  or  new  equipment  shall 
be  purchased,  the  decision  lying  with  the  board  of 
directors. 

Industrial  Establishments 

Whether  desirable  or  not,  such  detailed  supervision  of 
depreciation  is  not  always  found  in  industrial  establish- 
ments. Yet  the  interesting  facts  about  a  railroad  com- 


78  PRINCIPLES     OF    DEPRECIATION 

pany  do  not  differ  essentially  from  those  which  we  wish 
to  know  concerning  an  industrial  concern.  We  study 
both  from  similar  documents — the  balance  sheet  and  the 
statement  of  profit  and  loss — and  therein  the  vital  points 
are  similar.  Although  the  assets  are  different  in  form,-  it 
is  equally  important  that  they  be  protected;  and  although 
the  sources  of  income  differ,  the  percentage  of  net  profits 
measures  the  relative  success  of  the  undertakings. 

Present  and  Future  Conditions 

The  Interstate  Commerce  Commission  has  made  clear 
that  a  charge  may  be  made  for  repairs  or  renewals  even 
though  it  be  not  all  expended  within  the  period  covered 
by  the  statement  of  profit  and  loss.  The  Commission 
states  that  it  is  not  intended  to  say  that  the  entire  ac- 
cumulation of  a  year  must  be  expended  during  the  year.15 
This  simplifies  matters  greatly.  It  makes  it  possible  to 
write  off  a  developmental  expense  over  a  series  of  years; 
also  to  accumulate  a  fund  for  the  future  replacements  of 
expensive  material  assets. 

The  first  steps  having  been  taken  in  the  direction  of  a 
compulsory  depreciation  charge,  it  remains  to  be  seen 
how  far  the  reform  will  extend.  The  State  Utility  Com- 
missions are  seconding  the  Interstate  Commerce  Commis- 
sion by  introducing  in  their  work  the  principles  of  de- 
preciation. 

The  chief  factors  that  will  make  for  or  against  a  com- 
pulsory depreciation  charge  in  the  future  are: 

1.  The  general  theory  of  the  State's  relation  to  in- 

dustry. 

2.  The  efficiency  of  corporate  management  when  not 

interfered  with  by  the  State. 


15  Accounting  Series,  Circular  No.  13,  page  2. 


COURT    AND     COMMISSION     REGULATION 


79 


3.  The  tendency  of  industries  to  organize  in  a  way 

to  invite  control  by  commission. 

4.  The  attitude  of  professional  accountants  and  the 

candor  with  which  they  urge  that  which  the 
State  may  compel  if  they  fail. 


CHAPTER    VII 

THE  INCOME  TAX 

The  Income  Tax  in  England 

In  England  taxation  of  incomes  has  served  as  a  means 
of  raising  revenue  longer  than  in  the  United  States.  Before 
1878,  English  corporations,  in  the  determination  of  their 
taxable  incomes,  were  not  allowed  to  make  any  deduction 
from  income  to  cover  depreciation.  The  law  granted  the 
deduction  of  actual  expenditures  for  repairs  and  renewals, 
but  not  in  excess  of  the  average  expenditures  for  the  pre- 
ceding three  years.  Allowance  could  not  be  made  for  ex- 
isting depreciation  unless  money  had  been  paid  out  to  cover 
it.  In  1878  the  law  was  altered  to  permit  the  deduction  of 
a  reasonable  amount  for  the  diminished  value  of  machinery 
and  plant  resulting  from  wear  and  tear.  Depreciation  was 
not  mentioned  in  the  law,  nor  was  an  allowance  for  obso- 
lescence permissible.  Building's  were  not  specifically  men- 
tioned in  the  Act. 

In  1897  a  complaint  made  to  the  Chancellor  of  the  Ex- 
chequer brought  the  reply  that  no  objection  would  be  made 
to  a  deduction  from  the  assessable  profits  of  the  year  of  so 
much  of  the  replacement  cost  as  was  represented  by  the 
existing  value  of  the  replaced  machinery.  This  allows 
nothing  for  composite  depreciation.  The  Finance  Act  of 
1907  provides  that  no  allowance  can  be  made  in  excess  of 
an  amount  which,  when  added  to  previous  allowances, 
equals  in  amount  the  cost  of  the  plant  plus  any  additional 
capital  expenditures.  The  Finance  Act  of  1910  grants 
some  further  relief  in  the  way  of  allowances  for  main- 
tenance and  repair  of  land  and  farm  buildings. 

80 


THE    INCOME    TAX  gl 

English  Income  Tax  Decisions 

In  the  English  case  of  Knowles  v.  McAdam  (1877)  a 
deduction  from  the  income  of  a  mine  property  to  cover 
exhaustion  of  capital  was  permitted,  but  this  decision  was 
probably  reversed  in  the  case  of  Coltness  Iron  Company  v. 
Black  (1881),  where  the  charging  of  the  cost  of  sinking 
new  shafts  to  replace  old  ones  was  not  allowed.  It  seems, 
however,  that  there  is  no  objection  to  an  allowance  for  the 
cost  of  sinking  a  shaft  when  minerals  are  secured  therefrom 
which  are  a  source  of  profit  for  the  year  in  which  such 
shaft  is  sunk.  In  Coltness  Iron  Company  v.  Black  the  de- 
duction disallowed  did  not  represent  the  cost  of  shaft  sink- 
ing during  the  year,  but  rather  expenditure  on  borings  and 
shafts  exhausted  during  the  year.  The  latter  is  the  better 
basis,  so  the  situation  appears  unsatisfactory. 

The  Income  Tax  in  the  United  States 

The  first  income  tax  law  in  the  United  States  was  en- 
acted in  1861  and  repealed  in  1872.  A  tax  of  2%  on 
incomes  in  excess  of  $4,000  was  levied  by  act  of  Congress 
in  1894,  but  this  law  was  declared  unconstitutional.  In 
1909  the  so-called  Corporation  Tax  Law  was  passed. 
Although  nominally  an  excise  tax,  in  r»any  ways  it  re- 
sembled an  income  tax  limited  to  corporations. 

The  Corporation  Tax  of  1909 — Depreciation  Charges 

This  act  levied  a  tax  of  \%  upon  the  net  income  of 
corporations,  joint-stock  companies,  or  insurance  com- 
panies,-In  excess  of  $5,000.  In  arriving  at  the  net  income 
of  such  concerns,  deductions  were  allowed  for  expenses, 
interest,  taxes,  depreciation,  and  certain  other  items. 

In  returns  to  the  Commissioner  of  Internal  Revenue, 
the  amounts  allowed  for  depreciation  were  required  to  be 
stated  separately  from  other  losses.  Detailed  regulations 


82  PRINCIPLES    OF    DEPRECIATION 

were  promulgated  by  the  Treasury  Department.1  These 
provided  that  before  depreciation  could  be  allowed  it  must 
have  actually  occurred,  and  should  be  estimated  with  the 
aid  of  the  best  data  obtainable  from  other  similar  properties. 
The  depreciation  was  also  charged  off  on  the  books  of  the 
corporation  claiming  it.  It  was  not  necessary,  however, 
that  the  book  value  of  the  asset  be  itself  reduced,  for  by  a 
special  ruling  (May  9,  1912)  permission  was  given  to  make 
such  charges  in  the  form  of  a  nominal  reserve,  deductible 
from  the  corresponding  asset. 

The  Treasury  Department  ruled  that  the  deduction  for 
depreciation  should  be  based  on  four  considerations:  (1) 
the  lifetime  of  the  property,  (2)  its  cost,  (3)  its  value,  and 
(4)  its  use;  all  evidenced  by  ledger  entry  as  already  noted. 
It  is  worthy  of  mention  that  in  the  regulations  for  the  in- 
come tax  of  1913,  value  is  omitted  from  consideration, 
evidently  with  good  reason. 

The  Corporation  Tax  of  1909 — Stocks,  Bonds,  and  Real 
Estate 

Stocks  and  bonds  owned  could  be  adjusted  annually, 
such  adjustment  being  made  a  matter  of  ledger  entry,  and 
depreciation  or  appreciation  deducted  or  added,  as  the  case 
might  be.  Or,  if  held  as  permanent  investments,  no  account 
could  be  taken  of  them  until  disposed  of,  when  loss  or  gain 
over  original  investment  was  to  be  prorated  and  the  amount 
belonging  to  the  period  since  the  incidence  of  the  tax  added 
to  or  deducted  from  gross  income,  as  the  case  might  be. 
Increase  or  decrease  in  the  value  of  real  estate  sold,  when 
not  determinable  for  each  year,  could  be  similarly  prorated. 
Allowance  was  not  granted  for  premiums  on  stocks  and 
bonds  arbitrarily  charged  off.  The  shrinkage  must  have 
been  actual.  If  buildings  were  voluntarily  removed,  as  in 

1  Treasury  Decisions  1727,  1742,  1754,  and  1796. 


THE    INCOME,  TAX  83 

case  of  replacement,  the  resulting  loss,  if  not  covered  by 
depreciation  already  provided,  was  not  allowed,  but  was 
considered  as  entering  into  the  cost  of  the  new  structure. 
An  allowance  for  depreciation  of  the  corporation's  own 
stock  was  not  granted,  as  such  a  loss  was  not  that  of  the 
corporation  but  of  the  stockholders.  Identical  treatment  of 
stocks  and  bonds  is  not  altogether  proper,  nor  is  the  sug- 
gested method  of  bond  valuation  accurate.8 

The  Income  Tax  of  1913 

The  Excise  Tax  of  1909  has  been  superseded  by  the 
Income  Tax  of  1913.  An  amendment  to  the  Constitution 
has  removed  the  fundamental  objection  to  this  kind  of  tax, 
and  it  is  now  considered  a  fixed  part  of  our  fiscal  system. 
Section  2  of  the  Act  of  Congress,  October  3,  1913,  pro- 
vides, inter  alia,  that  the  net  income  of  corporations  and 
joint-stock  companies  shall  be  ascertained  by  deducting 
from  the  gross  income  received  from  all  sources  during  the 
fiscal  year:  first,  all  ordinary  and  necessary  expenses  paid 
during  the  year  in  maintenance  and  operation,  including 
rentals  of  property;  second,  all  losses  actually  sustained 
during  the  year  not  compensated  by  insurance  or  otherwise, 
including  a  reasonable  allowance  for  depreciation  arising 
from  use  and  wear  and  tear  of  property.  In  the  case  of 
mining  corporations,  the  law  also  grants  a  reasonable  allow- 
ance for  the  depletion  of  ores  and  all  other  material  deposits, 
not  in  excess  of  5%  of  the  gross  value,  at  the  mine,  of  the 
output  for  the  year  for  which  the  computation  is  made. 

In- 'the  case  of  corporations  existing  under  the  laws  of 
foreign  countries,  net  income  is  ascertained  by  deducting 
the  allowances,  including  depreciation,  from  the  gross  in- 
come accruing  within  the  year  from  investments  made  and 
business  transacted  in  the  United  States. 


2  See  Sprague's  "Accountancy  of  Investment." 


84  PRINCIPLES    OF    DEPRECIATION 

For  the  determination  of  the  income  of  individuals,  the 
wording  of  the  law,  with  respect  to  the  allowance  for 
depreciation,  is  slightly  different  than  for  corporations. 
For  these  latter  a  reasonable  allowance  is  granted  for 
depreciation  resulting  from  use  and  wear  and  tear  o'f 
property;  for  individuals  a  reasonable  allowance  is  granted 
for  depreciation  resulting  from  exhaustion  and  wear  and 
tear  of  property  arising  out  of  its  employment  in  business. 
The  difference  is  immaterial,  however,  and  is  not  recognized 
in  the  regulations  promulgated  by  the  Commissioner  of 
Internal  Revenue. 

Allowance  for  Exhaustion 

The  allowance  for  exhaustion  and  wear  is  for  such  as 
has  occurred  for  the  year  assessed,  not  for  preceding 
years.3  In  Addie  &  Sons  v.  Solicitor  of  Inland  Revenue,4 
it  was  held  that  no  deduction  could  be  made  for  pit  sinking 
or  for  depreciation  of  buildings  and  machinery.  In  Little 
Miami,  etc.,  R.  R.  v.  U.  S.,5  it  was  held  that  estimated  de- 
preciation of  assets  may  be  deducted.  Sums  carried  to  the 
surplus  or  contingent  fund  cannot  be  deducted,  though 
afterwards  lost.6  Sums  carried  to  account  of  a  repair  fund 
come  within  the  above,  and  cannot  be  deducted.7  In  Eng- 
land depreciation  of  machinery  due  to  removal  of  business 
is  a  capital  loss  and  not  deductible.8  In  Burnley  Steamship 
Co.  v.  Aikin,9  a  steamship  company  was  allowed  a  deduc- 
tion on  (1)  loss  of  earning  power  from  obsolescence,  and 
(2)  loss  of  market  value  from  wear  and  tear.  The  Knox- 
ville  Water  case  and  the  Consolidated  Gas  case  are  com- 


8  Clayton   v.   Newcastle-under-Lyme,  2  Tax  Gas.   416   (1888);    Hall  &  Co.   v. 
Rickman,  54  Week.  Rep.  380  (1906). 
4  1  Tax  Cas.   1    (1875). 
6  108  U.  S.  277;    27  L.  Ed.  724  (1883). 

6  Solicitor   General   Phillips,   14   Ops.   Atty.   Gen.   643    (1874). 

7  Ruling,  2  Int.   Rev.  Rec.   100. 

8  Smith  v.  Westinghouse   Brake  Co.,  2  Tax  Cas.  357. 
f;  Tax  Cas.  275    (1894). 


THE    INCOME    TAX  85 

mented  on  elsewhere.     Most  of  the  cases  are  English,  and 
so  may  not  be  a  precedent  for  American  courts. 

In  Great  Britain  the  owner  of  both  the  mine  and  the 
estate  of  which  the  mine  formed  a  part  was  not  allowed  a 
deduction  for  partial  exhaustion  of  the  mine.10  The  House 
of  Lords,  in  Coltness  Iron  Co.  v.  Black,11  held  that  a  mine 
owner  is  not  entitled  to  a  deduction  for  capital  expended  in 
making  bores  and  sinking  pits  which  had  been  exhausted  by 
the  year's  working,  thus  apparently  overruling  Knowles  v. 
McAdam.12  In  Bonner  v.  Bassett  Mines,  Ltd.,13  it  was  held 
that  it  was  wrong  to  allow  a  deduction  for  a  tin  mine  shaft 
sunk  fifty  fathoms  further  down  for  the  purpose  of  dis- 
covering lodes.  The  money  required  for  sinking  the  shaft 
was  held  to  be  a  capital  expenditure. 

Stratton's  Independence,  Ltd.,  v.  Howbert 

This  decision14  is  of  considerable  importance  in  deter- 
mining the  status  of  mining  corporations  under  the  income 
tax  law  and  deserves  special  attention.  Stratton's  Inde- 
pendence, Ltd.,  was  an  English  corporation  engaged  in 
mining  in  Colorado.  Suit  was  brought  in  the  District 
Court  of  the  United  States,  District  of  Colorado,15  by  the 
corporation  to  recover  taxes  paid  under  protest  to  the  Gov- 
ernment for  1909  and  1910,  under  the  Corporation  Tax 
Act  of  1909,  on  what  was  presumably  income  but  which  the 
corporation  declared  represented  depreciation  of  its  capital 
assets.  Briefly,  the  point  at  issue  was,  what  deductions 
should  the  corporation  be  permitted  to  make  from  gross 
income  in  order  to  arrive  at  taxable  net  income?  No 
question  was  raised  as  to  the  appropriateness  of  deducting 


0  Miller  v.  Fairie,   16  Scot.  L.  R.   189   (1878). 
»1   Tax   Cas.   287    (1881). 

2  26  Week.   Rep.   114    (1877). 

3  Law  Times,   Dec.   31,   1912,  page   179. 

4  L.   Ed.  Advance  Opinions,  Jan.   15,  1914. 

5  No.  5781. 


86  PRINCIPLES     OF    DEPRECIATION 

ordinary  expenses  of  operation.  Disagreement  arose  over 
the  amount  that  should  be  allowed  for  depreciation  of  capi- 
tal resulting  from  the  extraction  of  ores. 

It  is  agreed  that  income  for  purposes  of  dividends,  in 
case  of  mining  companies,  may  include  a  portion  of  fhe 
capital.16  Therefore,  the  District  Court  held  that  if  the  net 
income  for  dividend  purposes  is  not  affected  by  the  amount 
of  the  ores  extracted,  it  should  not  be  affected  for  purposes 
of  the  excise  tax.  From  this  and  other  statements  made  by 
the  court  in  this  case  the  inference  might  be  drawn  that  no 
allowance  whatever  could  be  made  for  depletion  of  minerals. 
Thus  the  court  suggests  that  the  practical  result  of  deduct- 
ing depreciation  of  ores  would  be  to  free  the  company  from 
payment  of  any  tax  whatever.  In  this  instance  such  would 
be  the  case,  because  the  company  held  that  the  depletion  of 
the  ores  amounted  to  their  actual  selling  price  after  being 
mined,  less  cost  of  extraction.  This  leaves  no  income  what- 
ever. It  seems  clear  that  the  court's  statement  that  depre- 
ciation as  applied  to  buildings,  etc.,  cannot  be  enlarged  to 
apply  to  ore  extracted,  is  made  in  view  of  the  particular 
claims  of  the  company. 

The  trial  was  based  on  an  agreed  statement  of  facts,  to 
wit :  that  for  the  year  1909  the  gross  sales  of  ores  amounted 
to  $284,682.85;  the  cost  of  extracting  the  same,  $190,- 
939.42 ;  and  that  .the  value  of  the  ores  thus  extracted  in 
1909  was  $93,743.43  when  still  in  the  mine.  In  other 
words,  the  difference  between  gross  sales  and  cost  of  ex- 
traction exactly  equaled  the  value  of  the  ores  before  ex- 
traction. The  facts  for  the  year  1910  were  similar. 

The  company  appealed  the  case  and  on  a  certificate 
from  the  Circuit  Court  of  Appeals  the  Supreme  Court  of 
the  United  States  affirmed  the  decision  of  the  lower  court. 
Being  made  upon  an  agreed  statement  of  fact,  this  decision 

16  See  Morawetz  on  Private  Corporations,  §  442. 


THE    INCOME    TAX  87 

is  in  no  way  opposed  to  the  Treasury  decision  permitting  a 
reasonable  deduction  for  the  depreciation  of  ores  on  the 
basis  of  their  value  in  toto,  or  on  the  basis  of  original  cost 
as  required  under  the  Income  Tax  of  1913.  The  Supreme 
Court  in  its  decision  states  that  a  definition  of  value  of  ore 
in  place  was  adopted  with  the  intention  of  excluding  any 
allowance  for  profit,  that  it  is  fallacious  to  assume  that  the 
ores  possessed  any  such  value  before  they  were  mined,  and 
that  property  is  to  be  valued  not  on  latent  or  occult  values, 
but  on  practical  considerations  affecting  market  value. 

No  depreciation  was  charged  on  the  mine's  books,  but 
the  court  did  not  express  an  opinion  as  to  whether  this  was 
a  matter  of  material  importance. 

Interpretation  of  the  Income  Tax  Law 

Under  the  Income  Tax  of  1913,  the  Commissioner  of 
Internal  Revenue  prescribes  that,  in  accordance  with  the 
law,  the  allowance  for  depreciation  from  exhaustion  and 
wear  and  tear  cannot,  in  the  case  of  mines,  exceed  5%  of 
the  gross  value  at  the  mine  of  the  year's  output.  This  does 
not  include  the  expense  of  restoring  property,  nor  can  it 
include  an  allowance  to  make  good  exhaustion  already 
allowed.  By  gross  value  at  the  mine  is  meant  the  actual 
market  value  of  the  output,  coal,  crude  oil,  etc.,  at  the  mine 
or  well  if  the  price  is  established  by  sale  at  that  place.  If 
established  at  some  other  place,  or  on  the  basis  of  bullion 
or  metallic  value,  then  such  established  value  less  transpor- 
tation,, reduction,  and  smelting  charges  is  held  to  represent 
gross  value  at  the  mine.17  The  depreciation  allowance  must 
be  based  upon  the  shrinkage  of  the  actual  investment,  and  in 
case  it  appears  that  the  established  allowance  may  return 
the  capital  invested  before  the  mine  is  exhausted,  the  allow- 
ance must  be  diminished  in  accordance  with  the  estimated 


17  Income  Tax  Regulations,  Acts  6  and  1-42. 


88  PRINCIPLES     OF    DEPRECIATION 

number  of  years  the  minerals  will  last.  If  the  capital  in- 
vested is  thus  returned  to  the  corporation  before  the 
minerals  are  exhausted,  no  further  deduction  shall  be  made. 

How  Deduction  is  Limited 

A  variation  exists  in  the  wording  of  the  law  in  its  appli- 
cation to  mines  owned  by  individuals  and  those  owned  by 
corporations.18  In  the  former  case  it  provides  a  reasonable 
allowance  for  exhaustion  and  wear  and  tear  of  property 
arising  out  of  its  use  or  employment  in  the  business,  not  to 
exceed  5%  of  the  gross  value  of  the  output  in  case  of 
mines.  But  for  corporations  it  says  all  losses  sustained, 
including  a  reasonable  allowance  for  depreciation  by  use 
and  wear  and  tear  of  property;  and  in  case  of  mines  a 
reasonable  allowance  for  depletion  of  ores  and  all  other 
natural  deposits,  not  to  exceed  6%  of  the  gross  value  of  the 
output.  The  former  would  seem  to  limit  the  total  deduc- 
tion for  depreciation  to  5%  of  the  gross  value  of  the  output 
at  the  mine;  while  the  latter  specifically  states  that  a  rea- 
sonable allowance  shall  be  deducted  for  depreciation  from 
use  and  wear  and  tear,  if  any,  and  an  allowance  for  deple- 
tion of  minerals,  not  in  excess  of  5%  of  the  gross  value  of 
the  output  at  the  mine.  Article  142  of  the  Income  Tax 
Regulations  indicates  that  in  the  interpretation  of  the  law 
no  such  distinction  should  be  made.  In  referring  to  the 
allowance  for  both  individuals  and  corporations  it  says  that 
if  such  rate  of  5%  will  tend  to  return  the  investment  before 
the  deposits  are  exhausted,  it  should  be  reduced.  Article 
143  of  the  regulations  specifically  grants  to  corporations  an 
allowance  for  depreciation  of  plant  over  and  above  the  5% 
for  depletion  of  ores.  There  is  no  reason  why  individuals 
should  be  given  less. 

Following  are  comments  on  the  regulations  supplied  by 

18  Income  Tax  Regulations,  Acts  6  and  142. 


THE    INCOME    TAX 


89 


the  Commissioner  of  Internal  Revenue.  Likenesses  and 
differences  in  the  administration  of  the  Income  Tax  of  1913 
and  the  Corporation  Tax  of  1909  are  noted. 

Sale  of  Capital  Assets 

In  case  of  property  acquired  after  January  1,  1909,  and 
later  disposed  of,  the  difference  between  cost  and  selling 
price  shall  constitute  an  addition  to  or  subtraction  from 
gross  income  of  the  year  in  which  the  property  is  sold,  ac- 
cording as  it  represents  a  loss  or  a  gain.  In  case  of  prop- 
erty acquired  before  January  1,  1909,  such  difference  be- 
tween cost  and  selling  price  should  be  prorated,  and  the 
amount  of  the  difference  applicable  to  the  period  since 
January  1,  1909,  added  to  or  deducted  from  gross  income 
of  the  year  in  which  the  sale  is  made,  accordingly  as  it  is  a 
gain  or  a  loss.19  This  is  the  same  provision  as  in  the  law 
of  1909. 

Good-Will 

No  allowance  is  granted  for  depreciation  of  good-will.20 
This  is  the  same  as  under  the  law  of  1909. 

Bad  Debts 

To  be  a  proper  deduction  they  must  be  charged  off  on 
the  books,  and  treated  as  income  if  later  collected.21  This 
is  the  same  as  under  law  of  1909. 

Reserve  for  Anticipated  Losses 

Not  a  proper  deduction.22 

Removal  of  Buildings 

If  not  already  charged  to  depreciation  the  loss  thus  in- 


19  Income  Tax  Regulations,  Art.  109. 

20  Ibid.,  Art.  136. 

21  Ibid.,  Art.  125. 
*  Ibid.,  Art.  126. 


90  PRINCIPLES     OF    DEPRECIATION 

curred  must  be  charged  to  the  new  structure.23    This  is  the 
same  as  under  law  of  1909.24 

Incidental  Repairs 

These  should  be  deducted  as  expenses.25 

Depreciation  Reserve 

The  depreciation  reserve  must  be  employed  only  for 
making  good,  losses  on  the  property  for  which  it  was  cre- 
ated. If  the  reserve  exceeds  the  required  amount  it  should 
be  restored  to  income.26  If  any  part  of  it  is  used  for  an- 
other purpose,  income  must  be  correspondingly  increased.27 

The  advisability  of  restricting  the  use  of  the  deprecia- 
tion reserve  to  the  renewal  of  losses  on  property  for  which 
it  was  created,  might  be  questioned.  It  is  clear,  however, 
that  the  purpose  of  this  clause  is  to  prevent  the  employment 
of  the  reserve  for  purposes  altogether  foreign  to  that  for 
which  it  was  intended,  making  its  legitimate  use  impossible. 

Bonds 

If  a  corporation  purchases  bonds  above  par  it  may  de- 
duct from  gross  income  an  amount  proportionate  to  the  life 
of  the  bond,  providing  this  amount  is  written  off  on  the 
books  so  that  the  book  value  will  equal  redemption  value 
when  the  bonds  fall  due.  The  amount  of  the  amortization 
must  be  proportioned  with  respect  to  three  things:  (1) 
purchase  price,  (2)  maturity  value,  and  (3)  time  of  ma- 
turity. When  bonds  are  issued  below  par,  and  must  be 
redeemed  at  par  when  they  mature,  the  loss  thus  sustained 
by  the  issuing  corporation  should  be  prorated  over  the  life 
of  the  bonds.28  Treasury  Decision  1742  also  permitted 


a  Income  Tax  Regulations,  Art.  127. 
"Treasury  Decision  1742. 
25  Income  Tax  Regulations,  Art.  131. 
28  Ibid.,  Art.  132. 

27  Ibid.,  Art.  133. 

28  Ibid.,  Art.  135. 


THE    INCOME    TAX  9! 

annual  additions  or  deductions  for  stocks  under  the  law  of 
1909.  These  are  discussed  under  the  "Sale  of  Capital 
Assets"  on  page  89. 

Patents 

The  investment  in  patents  is  made  up  of  the  cost  of  ob- 
taining them — fees,  drawings,  models,  etc.  Since  patents 
are  monopolies  granted  for  a  period  of  seventeen  years,  the 
amount  of  the  deduction  allowable  for  depreciation  of 
patents  should  be  one-seventeenth  of  their  actual  cash  cost. 
If  the  patent  is  bought  outright,  the  price  paid  therefor 
represents  its  cost.  If  paid  for  in  securities,  then  the  actual 
cash  value  of  the  securities  given  is  its  cost.29  If  a  patent 
becomes  worthless  before  the  end  of  the  seventeenth  year, 
that  part  of  its  cost  not  yet  deducted  may  be  deducted  from 
gross  income  in  the  year  in  which  the  fact  of  such  worth- 
lessness  is  discovered,  and  such  unreturned  value  shall  be 
such  part  of  original  cost  as  the  remaining  number  of  years 
the  patent  has  to  run  is  part  of  seventeen  years.30 

Timber  Land 

The  purpose  being  to  return  to  the  corporation  an 
amount  which,  added  to  salvage  value  of  land,  will  equal 
the  amount  actually  invested,  corporations  owning  timber 
lands  and  disposing  of  their  timber  will  be  allowed  such 
amounts  for  depletion  as  will  secure  to  themselves  their 
original  investment.31  Further  deductions  are  not  allow- 
able after  an  amount  equal  to  the  investment  less  salvage 
has  bee'n  returned.32 

Natural  Deposits,  Coal,  etc. 

Depreciation  must  be  based  on  actual  cost  of  such  de- 


28  Income  Tax  Regulations,  Art.  137. 

30  Ibid.,  Art.   138. 

31  Ibid.,  Art.   139. 

32  Ibid.,  Art.  140. 


92  PRINCIPLES     OF    DEPRECIATION 

posits.  Treasury  Decision  1742  instructed  corporations  to 
value  their  deposits  of  minerals,  etc.,  as  at  January  1,  1909, 
not  on  the  basis  of  ordinary  selling  value  less  whatever  it 
might  cost  to  do  the  mining,  as  was  done  in  Stratum's  In- 
dependence, Ltd.,  v.  Howbert,  but  on  the  basis  of  salable 
value  of  the  entire  deposit — en  bloc — as  at  that  date.  What- 
ever the  unearned  increment  at  that  date  might  be,  it  was 
to  be  excluded  from  the  item  of  gross  income.  Therefore, 
if  additional  minerals  are  discovered  later,  investment  cost 
may  be  returned  before  such  additional  minerals  are  ex- 
hausted. Further  deductions  should  then  be  discontinued. 
The  unearned  increment  is  altogether  neglected  by  the  later 
regulations  for  the  income  tax.33  When  the  mines  are 
operated  on  a  royalty  basis  no  deductions  can  be  claimed 
for  depreciation.34 


18  Income  Tax  Regulations,  Art.  146. 
«*  Ibid.,  Art.  145. 


CHAPTER    VIII 

VALUATIONS 

State's  Relation  to  Industry 

Today  the  valuation  of  the  properties  of  public  service 
corporations  for  purposes  of  rate-making,  purchase,  taxa- 
tion, and  capitalization  constitutes  an  important  function  of 
commissions  and  courts.  Industries  that  are  clothed  with 
a  public  interest  are  now  placed  in  a  separate  category, 
although  their  complete  legal  status  does  not  appear  as  yet 
to  be  definitely  outlined.  Some  fundamental  distinctions 
exist  between  them  and  ordinary  private  enterprises,  which 
necessitate  considerable  governmental  supervision  of  the 
former.  The  interest  of  the  public  is  directly  involved — 
consequently  the  need  of  safeguarding  it  by  some  form  of 
state  control. 

The  past  few  years  have  witnessed  a  remarkable  change 
in  the  relation  existing  between  the  State  and  these  public 
utilities.  It  was  formerly  thought  that  competition  was 
the  essential  regulating  factor  in  all  instances;  but 
monopoly  is  now  recognized  as  a  permanent  and  unavoid- 
able condition  with  which  the  Government  must  deal. 
Where  conditions  are  favorable,  competition  affords  the 
needed  forces  for  the  equitable  adjustment  of  rates.  Where 
rates  are  exorbitant,  competition  lowers  them  or  else 
eliminates  those  who  are  unable  to  sell  at  normal  prices. 
But  in  the  absence  of  competition  the  regulative  function  is 
more  and  more  coming  to  be  performed  by  the  State. 

Recent  Industrial  Changes 

Fifty  years  ago  many  of  the  modern  industrial  instittl- 

93 


94 


PRINCIPLES     OF    DEPRECIATION 


tions  were  either  unknown,  or  so  new  that  their  real  posi- 
tion in  relation  to  the  consumer  was  not  fully  appreciated. 
Transportation  facilities  were  so  needed  that  franchises, 
grants,  and  privileges  were  given  without  any  great  amount 
of  reflection  upon  the  ultimate  effect  of  such  action  upon 
the  community.  However,  with  the  great  industrial  de- 
velopment of  recent  years,  the  growth  of  cities,  the  altera- 
tions in  industrial  and  commercial  methods,  and  the  conse- 
quent changes  in  economic  theory  in  conformity  with  these 
newer  conditions,  it  has  been  found  necessary  to  scan  care- 
fully the  State's  relation  to  industry,  with  the  result  that 
today  the  control  of  public  utilities  by  the  State  is  univer- 
sally recognized  as  one  of  its  legitimate  functions.  This 
interference  finds  points  of  contact  in  the  State's  power  to 
tax  and  to  determine  an  equitable  charge  for  the  services 
which  the  various  public  utility  corporations  render.  - 

Taxation  of  Public  Utilities 

Taxes  are  essential  to  the  existence  of  government  and 
should  be  equitably  borne  by  the  property  whose  existence 
is  made  possible  and  perpetuated  by  the  protective  agency 
of  the  State.  Assessments  and  valuations  are  made  to  en- 
able the  State  to  levy  taxes,  which  are  just  in  proportion  to 
the  State's  ability  to  determine  the  equitable  basis  of  com- 
putation. The  problem  is  always  difficult  because  of  the 
difficulty  of  judging  property  values,  both  tangible  and  in- 
tangible. The  work  of  valuing  public  service  utilities  is 
peculiarly  difficult  because  of  the  complex  character  of  their 
physical  make-up,  the  difficulty  of  accounting  for  intangible 
values  and  of  giving  due  weight  to  depreciation,  the  un- 
earned increment  in  increasing  land  values,  etc. 

Public  Utility  Service 

Public  utilities  affect  the  welfare  of  the  people  whom 


VALUATIONS 


95 


they  serve,  through  quality  and  kind  of  service  offered  and 
charges  demanded.  Usually  they  possess  monopolistic 
franchises  granted  by  the  State  or  municipality.  Often- 
times they  are  exclusive  producers  of  a  service  because  an 
attempt  to  duplicate  this  work  results  in  disastrous  com- 
petition, or  is  impossible.  Two  characteristics  of  public 
utilities — monopolistic  form  and  extensive  public  service — 
make  commission  control  desirable.  Competition  cannot 
act  as  a  regulative  force,  since  it  leads  to  injurious  rate 
wars  and  expensive  duplication  of  works,  thus  sacrificing 
the  interests  of  the  public. 

Public  Service  Commissions 

The  state  railroad  commissioners  have  shown  the 
ability  of  the  State  to  control,  to  a  greater  or  less  degree, 
an  industry  of  a  quasi-public  character;  while  many  states 
now  have  public  service  commissions  which  were  formed  by 
expanding  the  power  and  jurisdiction  of  existing  commis- 
sions, or  were  newly  erected  by  legislative  enactment.  They 
are  clothed  with  plenary  powers  of  regulation  and  rate- 
making  over  the  various  public  service  corporations  en- 
gaged in  the  telephone,  telegraph,  street  railway,  water  and 
gas  supply  businesses,  collectively  known  as  public  utilities, 
and  adapted  to  control  by  commission  for  the  reasons  noted. 

Growth  of  Commission  Regulation 

Already  in  several  states  the  work  of  valuing  both  the 
physical  and  non-physical  properties  of  public  service  cor- 
porations has  been  extensively  undertaken.  Principles  gov- 
erning all  possible  cases  have  not  been  finally  promulgated, 
it  is  true,  but  much  has  been  accomplished  in  the  way  of 
establishing  sound  rules  of  procedure.  In  many  cases  prece- 
dent is  sufficiently  strong  and  authoritative  to  make  pos- 
sible a  statement  of  what  may  be  expected  to  be  the  future 


96 


PRINCIPLES     OF    DEPRECIATION 


policy.  In  other  cases  reports  and  decisions  are  conflicting, 
and  the  ultimate  outcome  must  depend  upon  further 
elucidation  of  the  matter  or  upon  the  decision  of  the 
Supreme  Court  of  the  United  States — or  both. 

Massachusetts  took  the  lead  with  the  formation  of  a 
board  of  railway  commissioners  and  with  the  organization 
in  1885  of  a  gas  and  electric  light  commission,  while  the 
control  of  telegraph  and  telephone  companies  was  placed 
in  the  hands  of  a  board  of  highway  commissioners.  Cor- 
porate capitalization  and  the  issuance  of  securities  nave 
occupied  chiefly  the  attention  of  the  Massachusetts  commis- 
sioners. Valuation  for  rate-making  was  exhaustively  made 
by  the  Minnesota  Railroad  and  Warehouse  Commission, 
created  in  1899,  while  the  Railroad  Commission  of  Texas, 
organized  in  1891,  has  sought  to  ascertain  the  reconstruc- 
tion value  of  the  railroad  bed,  track,  depots,  and  transpor- 
tation facilities  belonging  to  the  railroads  in  the  state.  In 
1907  New  York  established  two  public  service  commissions, 
having  control  of  railroads,  and  electric  and  gas  public 
service  utilities.  The  Public  Service  Commission  for  the 
First  District  has  jurisdiction  in  Greater  New  York,  while 
the  other  has  control  over  the  remainder  of  the  state,  in- 
cluding telephone  companies  within  New  York  City.  In 
1905  Wisconsin  placed  the  control  of  express  companies  in 
the  hands  of  her  Railroad  Commission,  and  later  placed 
under  its  control  practically  all  other  public  service  corpora- 
tions, thus  transforming  it  into  a  full-fledged  public  service 
commission.  Many  other  states  have  followed  the  example 
of  these  and  the  principle  of  commission  regulation  is  fully 
established. 

The  Valuation  Problem 

It  can  be  definitely  stated  that  a  differentiation  must  be 
made  among  valuations  for  different  purposes,  such  as  rate- 


VALUATIONS 


97 


making1,  purchase,  etc.,  but  it  is  sometimes  difficult  to  say 
just  how  the  differentiation  should  be  made.  Just  what 
values  ought  to  be  excluded  in  one  case  or  included  in  an- 
other, is  a  concrete  problem  that  can  be  solved  only  in  con- 
nection with  the  circumstances  of  each  individual  valuation. 
Taxation  valuations  must  not  be  confused  with  valuations 
for  purposes  of  capitalization,  or  valuations  for  rate-mak- 
ing. In  Texas  a  valuation  was  made  of  the  physical 
property  of  railroads  for  taxation  purposes,  but  the  Su- 
preme Court  of  the  United  States  declared  that  the  results 
could  not  be  used  for  rate-making  because  the  basis  of 
valuation  was  too  narrow  to  comprehend  all  the  elements 
of  value. 

It  is  often  admitted  that  tax  values  of  physical  property 
ought  to  be  stated  below  capitalization  values,  to  prevent 
overtaxation  of  tangible  property;  and  it  was  recently  dis- 
closed that  St.  Paul  tax  values  equal  about  60%  of  normal 
selling  prices.1  One  public  service  commission  states  that 
its  findings  for  capitalization  purposes  are  not  intended  for 
rate-making  purposes.2  A  corporation  may  perhaps  hold 
assets  for  speculation,  but  not  employ  them  in  providing  its 
customary  services  to  the  public.  Consequently  the  cor- 
poration may  not  be  justified  in  including  such  property 
with  that  upon  which  it  bases  its  rates,  although  it  ought  to 
pay  taxes  on  it.  Methods  and  results  of  one  valuation 
may  be  useful  in  another,  but  a  valuation  must  be  made  with 
a  view  to  its  particular  object. 

Deprecia'tion  in  Valuations 

It  follows  that,  from  the  standpoint  of  valuation,  cer- 
tain factors  may  or  may  not  be  of  weight.  Depreciation  is 


1  Supplement   to   the   Annual    Report    of   the   Railroad   and    Warehouse    Com- 
mission of  Minnesota,  Nov.  30,   1908,  page  16. 

2  P.    S.   C.   R.  (First   District,   New   York),  re   Reorganization   of  Metropolitan 
Street  Railway  Co.,  Case  No.  1305. 


Q8  PRINCIPLES     OF    DEPRECIATION 

an  important  factor  in  most  valuations  where  physical 
property  is  under  examination,  and  sometimes  even  in  the 
case  of  intangible  property.  It  would  appear  that  the  only 
question  as  to  the  inclusion  or  non-inclusion  of  deprecia- 
tion is  answered  when  we  have  determined  whether  items 
of  a  depreciating  character  are  to  be  included  or  omitted. 
Is  depreciation  a  condition  whose  weight  is  determined  by 
the  purpose  of  the  valuation,  or  is  it  absolute  and  inde- 
pendent of  the  purpose  for  which  the  valuation  is  made? 
Evidently  the  latter,  for  although  different  estimates  may 
be  made  of  its  amount,  this  is  due  to  disagreement  on  the 
part  of  those  who  do  the  valuing.  They  attempt  to  dis- 
cover, and  perhaps  disagree  upon  what  all  admit  to  be  in 
fact  the  same. 

This  granted,  the  problem  of  depreciation  remains  the 
same  under  all  circumstances,  whether  the  valuation  is  for 
rate-making,  taxation,  capitalization,  or  purchase.  Here 
depreciation  means  reduced  service  value,  and  is  usually 
measured  in  terms  of  dollars  and  cents.  It  will  be  the 
same  for  each  item,  although  items  that  are  included  in  one 
case  are  properly  omitted  in  another.  The  difference  is  not 
one  of  depreciation,  but  of  the  inclusion  or  exclusion  of 
depreciating  values. 

Depreciation  is  an  important  factor  in  valuations.  Its 
determination  is  a  different  problem  from  the  ordinary  one 
in  depreciation — writing  down  assets  and  creating  funds 
for  their  ultimate  replacement.  In  valuations  we  seek 
present  values — values  of  today — not  a  notation  of  depre- 
ciation over  long  intervals  with  a  view  to  ultimate  re- 
placement. The  worth  of  an  asset  at  some  particular  time 
in  its  life  has  not  much  bearing  on  ultimate  replacement. 
To  create  a  replacement  fund  we  need  know  only  lifetime 
and  replacement  cost.  Greater  rapidity  of  depreciation  may 
occur  early  or  late;  the  replacement  fund  can  nevertheless 


VALUATIONS 


99 


be  formed  by  equal  additions  each  year,  or  by  greater  or 
smaller  additions  during  either  the  earlier  or  later  years. 

By  this  is  not  meant  that  these  two  phases  of  the  de- 
preciation problem  are  entirely  separated  from  each  other. 
Rather  it  is  intended  to  show  wherein  they  differ  and  af- 
ford opportunity  for  comparison.  If  the  gradual  progress 
of  depreciation  could  be  accurately  measured  and  some  sys- 
tem employed  by  which  the  costs  of  the  increments  to  the 
replacement  fund  could  be  made  exactly  equal  to  the  costs 
of  the  losses  through  depreciation,  then  the  two  problems 
of  valuations  and  replacements  would  be  reduced  to  the 
same  basis.  Nor  is  it  intended  to  say  that  this  is  alto- 
gether impossible.  But  it  must  be  borne  in  mind  that  the 
amount  in  the  depreciation  fund  and  the  actual  depreciation 
need  not  of  necessity  equal  each  other,  and  certainly  in  most 
cases  where  a  fund  is  formed  by  any  of  the  methods  in 
vogue — sinking  fund,  reducing  balance,  etc. — they  will  not 
be  equal. 

Present  Value  vs.  Cost  of  Reproduction 

In  all  valuations  the  distinction  must  be  made  between 
cost  or  cost-to-reproduce  on  the  one  hand,  and  present 
value  on  the  other.  Usually  the  comparison  must  be  made 
between  cost-to-reproduce  and  present  value,  because 
original  cost  is  in  most  cases  difficult  to  learn.  Could  it  be 
learned,  it  would  not  be  just  to  utility  companies  to  deduct 
depreciation  from  original  cost  to  find  present  value,  for 
this  would  be  ignoring  appreciation  due  to  the  unearned 
increment  in  land,  etc.  For  purposes  of  replacement,  how- 
ever, original  cost  should  serve  as  the  basis  for  computa- 
tion of  the  replacement  fund. 

That  this  is  right  the  answer  to  the  following  proposi- 
tion will  indicate :  A  machine  cost  originally  $100  and  must 
be  replaced  after  ten  years,  at  which  time  an  identical 


100  PRINCIPLES    OF    DEPRECIATION 

machine  can  be  purchased  for  $150.  Should  the  deprecia- 
tion be  reckoned  on  the  basis  of  original  cost  or  of  replace- 
ment cost?  It  seems  clear  that  original  cost  ought  to  be 
the  basis.  To  use  replacement  cost  as  a  basis  would  permit 
the  amortization  of  $150,  whereas  only  $100  was  invested. 
It  would  be  presumptuous  to  assume  that  the  original 
machine,  which  cost  $100,  took  on  during  its  lifetime  an 
additional  $50  in  value  merely  because  it  will  cost  $150  to 
replace  it.  This  greater  cost  is  due  to  the  increase  in  labor 
cost,  cost  of  iron,  etc.,  which  in  no  way  affects  the  original 
machine  except  possibly  for  selling  purposes — usually  a 
remote  possibility.  The  additional  $50  put  in  the  new 
machine  is  an  increase  in  the  investment  and  should  be 
charged  to  betterments.  That  rates  ought  to  be  increased 
to  permit  a  reasonable  return  on  such  increases  in  the  in- 
vestment, is  granted;  but  the  increases  themselves  should 
not  be  paid  for  by  the  consumers.  Nor  does  this  mean  that 
increases  in  investment  arising  from  community  develop- 
ment, scarcity  of  land,  etc.,  cannot  be  considered  a  part  of 
the  investment  upon  which  a  return  may  be  allowed.  It 
simply  means  that  the  consumer  cannot  be  expected  to 
furnish  the  investment,  and  in  addition  replace  it  and  pro- 
vide a  reasonable  return  thereon  out  of  his  pocket. 

By  comparison  of  cost-to-reproduce  and  present  value, 
the  amount  of  depreciation  is  supposedly  found,  although 
this  overstates  depreciation  if  in  cost-of-reproduction  we 
include  increased  cost  of  replacing  wasting  assets.  -Such 
increase  is  not  depreciation  but  additional  investment,  as 
shown  in  the  preceding  paragraph. 

Present  value  plus  replacement  fund — if  it  exists — may 
not  equal  or  even  approximate  cost-to-reproduce,  although 
it  is  sometimes  assumed  that  it  does.  It  ought  not  if  wast- 
ing assets  can  be  replaced  only  at  increased  cost,  which  in- 
crease should  be  represented  by  additional  investment. 


VALUATIONS  IOi 

Whether  or  not  it  does  is  of  importance  in  making  replace- 
ments rather  than  in  making  valuations.  As  stated  in  the 
Metropolitan  reorganization  case,  the  problem  is  not  how 
to  meet  and  provide  for  decrease  in  values,  but  what  is  the 
fair  value  of  the  plant  at  present.3  Reserve  funds  may 
provide  ultimate  replacement  even  though  capital  remains 
impaired  to  a  considerable  extent  in  the  meantime,  which 
will  occur  unless  the  fund  accumulates  at  least  as  rapidly  as 
value  disappears. 

Depreciation  as  Affecting  Basis  for  Rates 

Depreciation  is  a  factor  which  determines  values,  and 
consequently  must  be  considered  in  fixing  an  equitable  basis 
for  rates.  To  appreciate  the  bearing  which  depreciation 
has  in  this  matter  it  is  necessary  to  keep  in  mind  the 
significance  of  the  several  bases  that  have  been  advocated 
for  the  making  of  rates.  These  are :  original  cost,  cost-to- 
reproduce,  and  cost-of-reproduction-less-depreciation. 

By  original  cost  is  meant  actual  money  investment  at 
the  time  of  acquisition  and  construction.  Although  this 
method  has  some  desirable  features,  it  is  generally  admitted 
that  it  cannot  be  adopted  as  a  basis  for  rates.  Good  ac- 
counting seeks  to  preserve  the  original  cost  figures,  but 
usually  these  are  lost  in  the  various  processes  of  reorganiza- 
tion, consolidation,  etc.  If  preserved,  they  should  be  used 
rather  to  assist  in  finding  an  equitable  basis  for  rates,  than 
in  being  made  to  serve  as  such  a  basis.  Discussion  centers 
chiefly  about  the  cost-to-reproduce  and  cost-of-reproduc- 
tion-fess-depreciation  methods. 

Cost-of-Reproduction  Basis 

Cost-of-reproduction  as  a  basis  for  rate-making  has 
been  and  is  still  held  to  be  the  true  basis  upon  which  to 

3 P.  S.  C.  R.  (First  District,  New  York),  Case  No.  1305,  page  155. 


102  PRINCIPLES    OF    DEPRECIATION 

determine  rates.  Those  who  uphold  this  method  assert 
that  a  distinction  must  be  made  between  the  efficiency  of  a 
utility  and  its  value  when  determined  for  purposes  of  sale; 
that  so  long  as  the  service  performed  is  equally  good  as 
when  the  utility  was  new,  it  is  immaterial  to  the  consumer 
what  the  extent  of  the  depreciation  amounts  to. 

That  depreciation  ordinarily  bears  little  or  no  relation 
to  efficiency  is  shown  in  Chapter  V,  "Depreciation  and 
Efficiency."  Depreciation  means  that  the  time  of  replace- 
ment is  approaching,  and  consequently  the  total  service 
value  of  the  thing  depreciated  is  less  than  when  new.  But 
its  efficiency  remains  unimpaired,  and  sometimes  even  in- 
creases as  the  result  of  adaptation  and  adjustment. 

One  of  the  most  ardent  advocates  of  the  cost-to-repro- 
duce  basis  is  A.  C.  Humphreys.4  As  an  illustration  he 
takes  the  ties  of  a  railroad  or  the  poles  of  a  telegraph  line. 
Assuming  that  these  have  an  average  life  of  ten  years,  and 
that  one-tenth  of  the  total  number  should  be  replaced  each 
year,  Mr.  Humphreys  says  that  it  is  maintained  by  some 
that  the  average  age  of  the  ties  or  poles  taken  together  is 
five  years,  and  that  therefore  50%  depreciation  should  be 
deducted  from  cost  of  reproduction  to  determine  the  proper 
basis  for  rates.  Mr.  Humphreys  says  that  while  such  a 
statement  may  be  correct  as  a  question  of  averages,  it  is 
entirely  without  warrant  as  a  basis  for  the  deduction  of 
50%  from  the  investment.  Such  a  procedure,  he  says,  is 
confiscation,  depriving  the  investor  of  a  return  on  one-half 
of  his  investment.  Rather,  the  only  thing  which  the  cus- 
tomer is  concerned  with  is  the  efficiency  of  the  service 
afforded,  and  if  this  is  kept  at  100%  there  can  be  no  reason 
for  reducing  fates. 

Mr.  Humphreys  further  suggests  that  if  a  deduction 

4  Depreciation :  Estimated  and  Actual;  Proceedings  of  the  American  Gas 
Institute,  Vol.  8,  Part  2,  page  521. 


VALUATIONS 

must  be  made  from  original  cost  to  cover  depreciation  such 
as  cannot  be  avoided  by  adequate  renewals,  then  an  amount 
equivalent  to  such  deduction  ought  to  be  added  to  the  ap- 
praisal as  an  item  of  cost,  just  as  interest  during  construc- 
tion and  other  items  of  intangible  character  are  included. 

The  reproduction-cost-new  theory  has  been  upheld  by 
the  following  additional  authorities :  Wisconsin  Railroad 
Commission  in  re  City  of  Whitewater  v.  Whitewater  Elec. 
Lt.  Co.,  Dec.  16,  1910;  re  Columbus  Ry.  &  Lt.  Co.  v.  City 
of  Columbus,  Ohio,  1906;  Massachusetts  Joint  Board  in 
Massachusetts  Appraisal  of  the  New  York,  New  Haven 
and  Hartford  Railroad,  1911 ;  also  by  C.  E.  Grunsky  in 
Appraisal  of  Public  Service  Properties  as  a  Basis  for  the 
Regulation  of  Rates  ;5  William  J.  Wilgus  in  Physical  Valua- 
tion of  Railroads  ;8  and  Henry  Floy  in  Valuation  of  Public 
Utility  Properties  (1912). 

Cost-of-Reproduction-Less-Depreciation  Basis 

The  reproduction-cost-less-depreciation  theory  has  been 
upheld  by  the  following  authorities :  Oklahoma  Supreme 
Court  in  re  Pioneer  Telephone  &  Telegraph  Co.  v.  Westen- 
haver,  Jan.  10,  1911;  New  York  Public  Service  Commis- 
sion, First  District,  in  re  Metropolitan  Street  Railway  Re- 
organization, Feb.  27,  1912 ;  and  by  the  Supreme  Court  of 
the  United  States;7  also  by  Robert  H.  Whitten  in  Valua- 
tion of  Public  Service  Corporations,  page  359,  New  York, 
1912;  and,  most  recently,  by  the  Special  Committee  of  the 
American  Society  of  Civil  Engineers  in  their  tentative  re- 
port 'on  Valuation  for  the  Purpose  of  Rate-Making.8 

8  Transactions  of  the  American  Society  of  Civil  Engineers,  Vol.  LXXV,  page 
770. 

8  Ibid.,  Vol.  LXXII,  page  203. 

TKnoxville  v.  Water  Co.,  212  U.  S.  1;    S3  L.  Ed   371  (Jan.  4,  1909). 

*  See  Engineering  News,  Jan.  29,  page  226,  and  Feb.  12,  page  350,  1914; 
also  Report  of  the  Special  Committee  to  Formulate  Principles  and  Methods  for 
the  Valuation  of  Railroad  Property  and  Other  Public  Utilities,  Dec.  1,  1913, 
page  49. 


104 


PRINCIPLES     OF    DEPRECIATION 


With  reference  to  the  statements  made  by  the  advocates 
of  the  reproduction-cost-new  theory,  the  above-mentioned 
committee  observes  that  these  writers  invariably  ignore  the 
fact  that  a  depreciation  allowance  is  a  return  of  a  part  of 
the  investment,  and  that  when  the  investment  is  thus  re- 
turned it  does  not  constitute  confiscation  to  make  depre- 
ciated value  the  basis  for  rates.  Nor,  says  this  committee, 
do  the  rates  necessarily  decrease  when  depreciated  value 
is  made  the  basis.  Although  it  is  true  that  in  case  of  a 
given  property  the  amount  applicable  to  dividends  grows 
less  as  the  property  grows  older,  this  is  altogether  proper; 
for  a  continually  increasing  amount  of  the  investment  has 
been  returned  to  the  investors,  and  has  been  used  in  making 
replacements  and  additions,  or  perhaps  is  temporarily 
placed  in  a  depreciation  fund,  with  the  result  that  the  entire 
original  investment  remains  intact  at  all  times. 

The  case  for  the  cost-of-reproduction-less-depreciation 
theory  is  stated  clearly  by  Mr.  Whitten.  He  says  that  this 
early  depreciation  of  possibly  15%,  which  we  have  called 
composite  depreciation,  is  properly  charged  to  earnings  as 
it  accrues.  However,  instead  of  being  placed  in  reserve 
when  it  can  never  be  used  for  the  object  for  which  it  was 
intended,  it  should  be  used  to  reduce  the  capital  to  the 
permanent  requirements  of  the  business.  While  this  is  not 
done  in  practice,  what  amounts  to  very  much  the  same 
thing  is  done;  i.e.,  the  funds  are  used  in  making  additions 
and  betterments.  Again,  Mr.  Whitten  suggests,  that  since 
the  service  of  a  public  utility  is  a  continuous  one,  and  can 
be  rendered  only  by  a  plant  the  parts  of  which  inevitably 
depreciate,  the  investment  cost  must  be  assumed  to  be  con- 
tinuous ;  and  while  at  first  thought  it  may  seem  that  a  uni- 
form investment  cost  can  be  secured  only  by  assuming  a 
uniform  capital  value,  this  would  be  true  only  so  far  as 
interest  and  profits  are  concerned,  but  would  not  give  a 


VALUATIONS 


105 


uniform  total  investment  cost.  Investment  cost  consists 
not  only  of  simple  interest  and  profits  on  the  investment, 
but  also  includes  cost  of  necessary  repairs,  renewals,  and 
replacements.  Since  this  latter  cost  is  greater  in  an  old 
than  in  a  new  system,  the  investment  cost  must  be  equalized 
by  making  the  charge  for  the  interest  and  profits  corre- 
spondingly less,  which  can  be  done  only  by  decreasing  the 
investment,  using  for  that  purpose  the  savings  made  dur- 
ing the  early  years  when  renewals  are  few. 

Rates  will  not  be  reduced  because  of  the  depreciated 
value  of  the  old  plant,  for  with  the  increased  expenditures 
for  repairs,  renewals,  and  replacements  rates  would  other- 
wise have  to  be  increased.  This  can  be  avoided  only  by 
reducing  the  capital,  and  consequently  the  charge  for  in- 
terest and  profits.  In  this  way  investment  cost  and  charge 
are  made  uniform. 

Equitable  Basis  of  Rate-Making 

The  division  of  opinion  as  to  the  proper  basis  for  rate- 
making  is  partly  due  to  the  apparent  conflict  of  interest 
between  the  public  service  corporations  and  the  people. 
That  there  is  an  equitable  ground  upon  which  to  base  rates 
could  hardly  be  questioned.  Integrity  of  investment  must 
be  observed,  and  any  system  of  valuation  that  leads  to  con- 
fiscation is  unjust.  Investors  and  the  people  are  both  sub- 
ject to  imposition.  The  investor  should  afford  suitable 
service  and  the  people  should  pay  therefor  a  price  suffi- 
cient npt  only  to  return  to  the  investor  his  capital,  or  pre- 
vent it  from  wasting,  but  also  to  afford  him  ample  reward 
for  his  work  in  addition  to  the  normal  rate  of  interest  on 
his  money.  No  investor  could  ask  for  more;  certainly  the 
people  should  not  be  compelled  to  pay  more.  If  a  portion 
of  the  capital  is  returned  to  the  stockholders  in  the  form  of 
dividends  or  by  returning  a  portion  of  the  company's  se- 


I06  PRINCIPLES    OF    DEPRECIATION 

curities,  it  would  not  be  just  to  include  the  amount  of  such 
amortization  for  valuation  purposes.  The  suggestion  of 
Humphreys — that  so  long  as  service  is  efficient  it  is  not  the 
concern  of  the  public  what  the  amount  of  depreciation  may 
amount  to,  since  the  proprietors  are  under  obligations  to 
make  all  necessary  renewals  and  replacements — does  not 
appear  very  logical.  Who  can  compel  the  stockholders  of 
a  utilities  company  to  make  further  payments  into  the 
treasury  after  their  stock  is  full  paid?  How  else  have  re- 
placements, too  long  deferred  and  unprovided  for,  been 
made  than  by  the  issue  of  bonds  to  secure  the  funds  that 
should  have  been  provided  out  of  revenue,  thus  placing  cor- 
porations under  the  permanent  disability  of  large  fixed  in- 
terest charges? 

Rates  Not  Made  Lower  When  Investment  is  Reduced 

Those  who  uphold  the  cost-new  theory  do  so  from  the 
belief  that  if  the  cost-new-less-depreciation  plan  is  adopted, 
the  rates  will  be  made  lower.  But  such  would  be  the  case 
only  for  the  corporation  as  a  whole,  not  for  the  security 
holders,  since  a  portion  of  capital  has  been  amortized  and 
therefore  permanently  withdrawn  from  the  business.  If, 
on  the  other  hand,  the  amount  representing  this  unavoid- 
able depreciation  is  retained  by  being  reinvested  in  the  form 
of  additions  and  betterments,  the  capital  would  remain  the 
same.  It  would  not  represent  an  additional  investment  but 
merely  a  transfer  of  a  portion  of  the  capital  from  one  form 
to  another.  Additional  investments  should  come  from  the 
investors,  not  from  the  revenues  of  the  company,  and 
should  be  made  out  of  net  profits  rather  than  from  gross 
income  before  net  profits  are  determined. 

Valuations  for  Purposes  Other  Than  Rate-Making 

Valuations  for  rate-making  at  present  occupy  the  pub- 


VALUATIONS 


107 


lie  attention  more  than  valuations  for  other  purposes. 
Nevertheless  other  valuations  are  of  great  importance.  No 
doubt  the  present  valuation  of  railroads  being  undertaken 
by  the  Interstate  Commerce  Commission  will  be  found 
useful  for  a  number  of  different  purposes,  including  rate- 
making,  capitalization,  and  taxation. 

In  the  Metropolitan  reorganization  case  the  valuation 
was  for  capitalization  purposes.  Here  obsolescence  or 
supersession  as  one  phase  of  depreciation  was  considered, 
and  the  folly  of  retaining  obsolete  or  obsolescent  property 
at  original  cost  figures  was  shown.  Within  a  period  of 
twenty  years  many  miles  of  track,  once  constituting  the 
most  valuable  lines,  had  fallen  into  disuse.  One  constituent 
company  with  outstanding  bonds  amounting  to  one  million 
dollars  par  value  could  neither  sell  nor  lease  its  track,  nor 
get  money  to  carry  on  operations.  Obsolescence  was  well 
illustrated  by  the  inefficiency  of  the  horse  car  lines.  These 
lines  constructed  eighteen  years  before  valuation  were  said 
to  have  seventeen  years  of  service  remaining,  although  the 
system  was  in  fact  obsolete  and  impractical.  According  to 
testimony,  a  certain  sum  set  aside  or  expended  annually 
would  furnish  renewals  indefinitely  and  keep  up  the  old 
horse  car  system.  But  merely  making  provision  for  the  up- 
keep of  an  old  horse  car  road  was  in  this  instance  not  con- 
sidered good  business  policy. 

Failure  to  make  provision  for  future  replacement  of 
existing  equipment  by  more  up-to-date  equipment  necessi- 
tated the  issue  of  new  securities  for  the  purchase  of  electric 
equipment,  and  this  resulted  in  overcapitalization.  Values 
once  amounting  to  many  millions  of  dollars  had  ceased  to 
exist.  The  company  held  that  these  values  should  not  be 
written  off  because  allowance  had  been  made  for  develop- 
mental expenditures  in  certain  rate  cases,  although  no 
visible  evidence  thereof  remained.  But  this  was  not  a  rate 


108  PRINCIPLES     OF    DEPRECIATION 

case.  The  question  was,  to  what  extent  should  securities  be 
amortized;  and  the  Commission  rightly  contended  that 
securities  held  for  property  now  non-existent  should  be 
amortized.9  Nor  is  it  probable  that  such  non-existent 
values  would  have  been  granted  a  place  as  developmental 
expenditures  in  a  rate  case. 

Inadequate  Allowance  for  Depreciation 

Various  valuations  made  by  commissioners  indicate 
what  inadequate  steps  are  taken  to  forestall  depreciation 
and  obsolescence.  In  the  Queens  Borough  Gas  and  Electric 
case,10  the  New  York  Commission  for  the  First  District 
found  this  situation :  reproduction  cost,  $1,608,492 ;  present 
value,  $1,139,812;  depreciation,  $468,680.  Depreciation 
due  to  wear  and  tear,  or  physical  depreciation  only,  is  indi- 
cated, no  allowance  being  made  for  future  abandonments  or 
supersessions  consequent  upon  discoveries,  inventions,  im- 
proved processes,  or  functional  depreciation.  The  wide 
margin  between  reproduction  cost  and  present  value  re- 
sulted largely  from  failure  to  establish  adequate  deprecia- 
tion reserves. 

Depreciation  Found  on  Basis  of  Averages 

Equipment,  structures,  material,  etc.,  inevitably  depre- 
ciate, and  various  methods  have  been  employed  to  indicate 
the  extent  to  which  at  a  specified  time  depreciation  has 
occurred.  In-  Michigan  and  Wisconsin,  where  valuations 
were  made  by  tax  commissioners,  estimates  were  made  of 
the  present  value  of  each  unit.  In  Michigan  more  than 
40,000  freight  cars  were  thus  inspected.  A  more  econom- 
ical and  more  accurate  method  was  employed  by  the  Rail- 
road Commission  of  Washington.  Mortality  tables  of 


8  P.  S.  C.  R.  (First  District,  New  York),  Case  No.  1305,  page  159. 

10  P.  S.  C.  R.  (First  District,  New  York),  Order  and  Opinion  of  June  23,  1911. 


VALUATIONS 


109 


structures,  working  upon  the  same  principles  as  life  mor- 
tality tables,  were  used.  Experience  shows  that  similar 
structures,  units  of  equipment,  etc.,  have  a  definite  average 
lifetime.  Thus  the  average  life  of  freight  cars  is  approxi- 
mately twenty-five  years,  the  cars  losing  on  an  average  of 
about  4%  of  their  value  each  year.  By  multiplying  the  age 
in  years  by  4,  the  percentage  of  value  which  has  expired  is 
ascertained.  This  is  then  subtracted  from  100,  the  re- 
mainder showing  what  percentage  the  present  value  is 
of  original  cost.  To  make  possible  the  employment  of 
this  method,  date  of  construction  and  cost  new  must  be 
known. 

Appreciation 

Appreciation  occurs  in  certain  classes  of  assets,  and 
should  be  given  due  weight  in  valuations.  The  roadbed  of 
a  railway  appreciates  during  the  first  few  years,  when  it  is 
necessary  to  make  repairs  on  account  of  inequalities  and 
defects  resulting  from  sinking,  sliding,  etc.,  and  these  re- 
pairs are  charged  to  operation,  although  they  are  really 
capital  expenditures.  Additions  of  earth  and  stone  are  re- 
quired, and  the  roadbed  slowly  grows  firmer  and  safer  as 
the  old  material  becomes  more  compact.  Allowance  may 
be  made  for  this  by  entering  the  value  due  to  adaptation  and 
solidification  under  a  separate  head  representing  apprecia- 
tion after  operating  begins. 

The  Minnesota  Commission  allowed  over  10%  of 
original  cost  for  this  item  upon  lines  of  the  Northern 
Pacific  "aggregating  over  1,500  miles;  while  upon  lines  of 
the  Minneapolis  Western  Railway,  with  a  mileage  of  6.89 
miles,  it  allowed  but  slightly  over  \%.  The  difference  in 
the  two  cases  was  due  to  the  better  seasoning  of  the  road- 
bed of  the  Northern  Pacific.  The  Washington  Commis- 
sion says  that  appreciation  continues  about  five  years,  when 


IIO  PRINCIPLES     OF    DEPRECIATION 

the  value  of  the  roadbed  is  approximately  10%  greater 
than  when  new.11 

If  we  may  believe  the  statement  of  the  New  York  Com- 
mission for  the  First  District,  appreciation  is  a  simpler 
matter,  and  more  easily  handled,  than  depreciation.  It  says 
that  if  property  grows  in  value,  the  investor  has  no  cause 
for  worry;  and  if  the  State  recognizes  his  right  to  a  fair 
return  upon  the  increased  values,  he  is  adequately  protected. 
It  is  unnecessary,  says  the  Commission,  that  the  increase  be 
represented  by  securities,  and  further  that  if  earning  power 
is  present,  the  holder  of  securities  receives  an  adequate  re- 
turn regardless  of  the  amount  of  these  securities.  But  can 
the  matter  of  securities  be  so  lightly  brushed  aside  ?  It  may 
be  true  that,  as  was  stated  by  the  Railroad  Securities  Com- 
mission, the  amount  of  the  stocks  and  bonds  is  a  matter  of 
historical  importance  only,  and  par  value  is  not  a  measure 
of  actual  value.  But  does  this  mean  that  the  amount  and 
par  value  of  the  securities  are  matters  of  no  consequence? 
From  the  accountant's  standpoint,  the  amount  and  par  value 
of  the  securities  present  several  considerations  of  the  utmost 
importance. 

In  Smyth  v.  Ames,12  the  Supreme  Court  of  the  United 
States  held  that,  to  ascertain  the  fair  value  of  a  property, 
among  other  things  to  be  considered  are  the  amount  and 
market  value  of  its  stocks  and  bonds.  Certainly  market 
value  of  stock  does  afford  a  basis  for  judging  value,  even 
though  par  value  does  not. 

Recent  valuations  have  done  much  for  our  enlighten- 
ment on  depreciation  in  its  various  phases.  Consideration 
of  its  principles  in  the  work  of  valuation  has  indirectly 
shown  the  need  of  more  scientific  accounting,  such  as  the 


"  Finding  of  Fact  by  the  Railroad  Commission  of  Washington  Relative  to  the 
Valuation  of  Railroads,  page  164. 
"169  U.  S.  466. 


VALUATIONS 

establishment  of  adequate  reserves  for  replacements ;  and  the 
result  of  neglect  and  carelessness  in  this  matter  has  been 
shown.  Much  remains  to  be  done  in  the  way  of  removing 
doubtful  matters  from  their  present  tentative  situation. 


CHAPTER    IX 

LAND    IN    VALUATIONS 

Land  Not  a  Wasting  Asset 

Land,  possessing  some  unique  qualities,  may  be  con- 
sidered separately.  It  is  not  a  wasting  asset.  Land 
normally  appreciates,  not  through  alterations  in  physical 
textures  or  arrangement,  but  because  of  scarcity,  location, 
or  the  impossibility  of  duplication. 

The  wide  variations  in  the  results  arrived  at  by  ex- 
perts in  the  valuation  of  land  indicate  the  difficulty  of  the 
problem.  The  question  of  the  unearned  increment  be- 
comes of  vital  importance  in  public  utility  valuations,  for 
upon  the  determination  of  the  rightful  owner  of  this 
increment  must  to  a  large  extent  depend  the  amount  of 
the  charges  that  may  be  asked.  Under  our  present  order 
of  society  this  unearned  increment  belongs,  rightly  or  not, 
to  the  fortunate  .possessor  of  land  and  may  be  regarded  as 
a  reward  offsetting  misfortunes  in  other  directions.  Never- 
theless, there  is  a  noticeable  tendency  to  limit  the  amount 
of  the  rates  that  may  be  based  on  the  unearned  increment 
in  the  case  of  public  utilities.  Such  limitation  will  presum- 
ably find  its  compensation  in  franchise  privileges,  monop- 
oly, and  right  of  eminent  domain. 

Land  Values  That  May  be  Included 

Whether  or  not  land  and  appreciating  land  values 
ought  to  be  considered  in  valuations  depends  on  the  pur- 
pose of  the  valuation.  Where  a  public  utility  corporation 
possessed  several  tracts  of  land,  it  was  held  that  only  those 
actually  and  necessarily  devoted  to  public  use  could  be 

112 


LAND    IN    VALUATIONS 

included  for  rate-making  purposes.  This  despite  the  fact 
that  rising  land  values  may  make  it  wise  for  the  utility 
corporation  to  purchase  lands  that  may  not  be  "used  and 
useful"  in  its  service  to  the  public  for  some  time  to  come. 
The  situation  may  justify  such  a  purchase,  but  not  the  Jn- 
clusion  of  the  value  thereof  for  rate-making,  although  it 
ought  to  be  included  in  values  for  taxation. 

Attitude  of  Courts 

We  have  the  authority  of  the  Supreme  Court  of  Min- 
nesota in  Steenerson  v.  Great  Northern  Ry.  Co.,1  that  a 
railroad  is  entitled  to  earn  a  fair  return  on  the  cost  of  re- 
production of  its  property;  also  the  authority  of  the 
Supreme  Court  of  the  United  States  in  Willcox  v.  Consoli- 
dated Gas  Company,  that,  if  property  legally  entering  into 
the  consideration  of  the  rate  question  has  increased  in  value 
since  acquisition,  the  company  is  entitled  to  the  benefit  of 
the  increase ;  adding,  however,  that  this  is  the  general  rule, 
and  that  there  may  be  exceptions  where  the  property  may 
have  increased  so  greatly  in  value  that  a  rate  affording  a 
reasonable  return  upon  such  increased  value  may  be  unjust 
to  the  public.  (212  U.  S.  19.) 

Attitude  of  Interstate  Commerce  Commission 

Thus  there  appears  to  be  a  limit  to  the  growth  of  values 
upon  which  a  public  service  corporation  is  entitled  to  what 
is  called  a  fair  return.  There  is  a  common  tendency  on 
the  part  of  courts  and  commissions  to  place  a  limitation 
upon  increasing  values  for  rate-making  purposes.  The  In- 
terstate Commerce  Commission  faced  this  question  in  its 
investigation  of  advances  in  rates  by  carriers  in  western 
trunk  line  territory.2  Railway  officials  declared  that  they 


1  69  Minn.  353  (1897).     The  same  attitude  is  taken  in  the  more  recent  case  of 
Shepard  v.  Northern  Pacific  Ry.  Co.,  184  Fed.  765   (1911). 

2  Opinion  No.  1509,  decided  Feb.  22,  1911. 


PRINCIPLES    OF    DEPRECIATION 

possessed  a  "legal  right"  to  a  fair  return,  not  on  the  original 
investment,  but  on  the  estimated  present  value,  resulting 
largely  from  increase  in  land  values  and  amounting  to 
many  millions  of  dollars.  Admitting  the  great  services  of 
the  railroad  to  the  State,  the  Commission  asked  whether 
larger  income  should  not  be  derived  from  increased  traffic 
rather  than  from  heavier  tolls  on  those  already  served. 
Public  service  corporations  do  business  with  the  expectation 
of  deriving  an  income  from  services  rendered  to  the  public, 
not  from  investments  in  land  whose  value  happens  to  be 
increasing.  Whatever  may  be  the  true  economic  or  legal 
view  on  the  right  of  a  carrier  to  earn  a  reasonable  return 
on  the  increased  value  of  its  land,  says  the  Commission  in 
substance,  such  an  increase  does  not  of  itself  afford  the  basis 
for  an  increase  in  rates  upon  a  given  service.  This  may  be 
interpreted  as  leaving  the  question  unsettled,  since  average 
rates  may  be  made  to  furnish  a  fair  return  on  increased 
values  even  though  certain  specific  rates  do  not. 

Attitude  of  Minnesota  Commission 

It  is  the  belief  of  the  Minnesota  Railroad  and  Ware- 
house Commission  that  if  railroads  are  permitted  to  realize 
on  continually  increasing  land  values  by  employing  them  as 
a  basis  for  computing  returns,  they  will  ultimately  absorb 
a  disproportionate  share  of  the  country's  wealth.3 

Unusual  Interpretation  of  Cost-of-Reproduction 

The  cost-of-reproduction  method  of  valuing  land  has  on 
certain  occasions  been  given  an  unusual  interpretation. 
Railroad  officials  have  argued  that  land  owned  by  their 
companies  ought  not  to  be  valued  at  present  market  value, 
because  the  railroads,  were  they  actually  to  buy  the  lands, 
would  pay  more  than  market  value.  So  this  additional  cost 

8  Supplement  to  Annual  Report,  Nov.  30,   1908,  pages  iv-v. 


LAND    IN    VALUATIONS 

is  added  to  market  value  to  determine  cost  to  replace.  That 
railroads  do  pay  exorbitant  prices  for  land  is  well  known. 
This  is  because  of  injury  resulting  to  contiguous  property, 
and  because  land  owners  sometimes  look  with  disfavor  upon 
the  projected  road  and  take  the  opportunity  to  fleece  the 
company. 

If  land  is  valued  on  this  basis,  a  certain  multiple  of 
market  value  must  be  taken  to  arrive  at  reproduction  cost. 
In  Minnesota,  investigation  of  a  section  of  the  Illinois  Cen- 
tral indicated  that  of  35%  of  the  right  of  way  secured  by 
condemnation  the  company  paid  about  4^  times  average 
true  value,  while  of  the  65  %  purchase  by  agreement  the 
price  was  1.7  times  average  true  value.  Terminal  lands  in 
St.  Louis  cost  1%,  in  Minneapolis  1^,  and  in  Duluth  1J4 
times  normal  value. 

But  when  allowance  has  been  made  for  actual  excessive 
cost  of  land  to  railroads,  it  does  not  necessarily  follow  that 
they  may  write  up  these  lands  by  the  same  multiple  above 
present  market  values.  Value  as  utility  may  be  a  more  im- 
portant consideration  than  reproduction  cost  in  some  cases, 
and,  for  rate-making  purposes  at  least,  extremely  high 
valuations  of  property  cannot  be  accepted  merely  because 
it  could  not  be  reproduced,  or,  if  it  could,  only  at  very  high 
prices.  To  establish  original  cost  the  railroad  multiple 
should  be  used;  also  to  establish  cost  of  reproduction,  and 
appreciation.  But  full  cost  of  reproduction  may  not  be 
allowed  as  a  basis  for  rates. 

Sales  Method 

The  so-called  "sales  method"  of  determining  present 
value  has  its  uses  and  limitations.  It  is  based  on  the 
assumption  that  as  the  assessed  valuation  of  surrounding 
properties  is  to  real  value,  so  the  assessed  value  of  the 
property  in  question  is  to  its  real  value.  Thus,  if  land  in 


H6  PRINCIPLES    OF    DEPRECIATION 

a  city  is  assessed  at  60%  of  selling  price,  and  a  railroad 
buys  40  acres  of  land  within  the  city  limits  for  $12,000, 
the  same  land  being  assessed  at  $6,000,  then  the  normal 
selling  value  would  approximate  $6,000  -^-.60,  or  $10,000. 
So  the  railroad  paid  $2,000  above  normal.  The  efficacy 
of  this  method  is  dependent  on  two  conditions:  (1)  a  suffi- 
cient number  and  variety  of  transfers  to  afford  an  accurate 
statement  of  average  values,  and  (2)  the  equity  of  the 
assessed  valuations.  But  inequality  of  assessment  is 
notorious,  and  it  seems  that  the  method  can  be  employed 
only  within  rather  narrow  limits  and  then  may  well  be 
checked  up  with  any  other  available  information  concerning 
the  property  in  question. 

Allowances  to  be  Made 

The  special  committee  on  valuation  of  the  American 
Society  of  Civil  Engineers  believes  that  the  present  value 
of  the  land  ought  to  be  based  upon  actual  cost  plus  subse- 
quent appreciation.  This  appreciation  is  to  correspond  to 
that  of  surrounding  property;  and  if  the  valuation  cannot 
be  made  in  this  way,  the  land  is  best  valued  on  the  basis  of 
current  prices  of  neighboring  land  of  similar  character, 
increased  by  the  ratio  ordinarily  existing  in  that  section 
between  land  bought  by  public  service  corporations,  and  that 
purchased  by  private  parties.  Furthermore,  the  land  is  to 
be  subject  to  the  value  of  improvements  existing  upon  it 
when  it  was  purchased,  such  improvements  to  be  valued  at 
current  prices.4 

Appreciation  Considered  as  Income 

The  appreciation  of  land  values  is  apt  to  be  considered 
in  the  same  light  as  is  depreciation  of  other  kinds  of  assets. 
The  United  States  Circuit  Court  in  Consolidated  Gas  Co.  v. 


4  Report  of  the  Special  Committee,  page  52. 


LAND    IN    VALUATIONS 

City  of  New  York5  in  considering  this  matter  says  that 
appreciation  and  depreciation  should  be  considered  alike, 
and  in  expanding  upon  this  principle  the  New  York  Public 
Service  Commission,  First  District,6  says  that  the  only 
difference  is  that  while  depreciation  is  a  loss  to  be  debited, 
appreciation  is  a  profit  to  be  credited,  since  it  represents  an 
increase  in  assets.  The  Commission  thinks  that  if  land  is 
taken  at  its  depreciated  value  when  it  has  depreciated,  it  is 
only  fair  to  take  it  at  its  appreciated  value  under  opposite 
conditions.  To  accomplish  this  it  is  suggested  that  an 
entry  be  made  in  the  estimated  receipts  equal  to  average 
annual  appreciation;  otherwise,  while  the  consumer  is 
burdened  with  the  depreciation  of  all  other  items,  he  will 
not  receive  any  benefit  from  the  appreciation  of  the  land. 

Appreciation  Limited  by  the  Supreme  Court 

Justice  Hughes,  in  delivering  the  opinion  of  the 
Supreme  Court  of  the  United  States,  June  9,  1913,  in  the 
Minnesota  Rate  Cases,7  apparently  upholds  the  stand  taken 
by  the  Interstate  Commerce  Commission  in  the  railroad 
rate  cases  already  considered.  Declaring  the  cost-of-repro~ 
duction  method  inapplicable  in  the  case  in  hand  because  of 
the  conjectural  results  that  would  be  secured,  he  asks 
whether  in  determining  the  fair  present  value  of  a  railroad 
company's  property  as  a  basis  for  rates  it  is  proper  to  value 
its  right-of-way  in  excess  of  the  market  value  of  contiguous 
property  similarly  situated,  i.e.,  whether  such  an  increment 
of  value  is  to  be  added  as  will  not  only  cover  increase  in 
value*  resulting  from  the  activities  and  prosperity  of  the 
community,  but  will  constantly  outstrip  such  increase  in  all 
neighboring  lands. 

«157  Fed.  Rep.  855. 

s  Re  Gas  and  Electric  Rates  of  the  Queens  Borough  Gas  and  Elec.  Co., 
2  P.  S.  C.  R.  (First  District),  June  23,  1911. 

7  Simpson  et  al.  v.  Shepard;  Same  v.  Kennedy;  Same  v.  Shillaber;  230  U.  S. 
352. 


H8  PRINCIPLES    OF    DEPRECIATION 

The  court  concludes  that  the  increased  valuation  to  be 
permitted  should  not  exceed  average  normal  increase  of 
other  land  in  the  community. 

Old  vs.  New  Value 

It  has  been  suggested  that  land  acquires  a  special  value 
by  reason  of  the  fact  that  it  is  peculiarly  adapted  to  railroad 
or  other  public  utility  use.  In  such  cases  the  question  arises 
as  to  whether  the  owner  of  such  land  should  receive  com- 
pensation for  the  land  on  the  basis  of  its  value  to  him,  or  on 
the  basis  of  its  value  in  its  newer  function.  On  this  point 
the  United  States  Supreme  Court  maintains  that  it  is  the 
fair  market  value,  the  value  lost  by  the  owner,  rather  than 
the  value  gained  by  the  taker  that  must  be  accepted.8  This 
is  no  doubt  the  best  policy  to  be  pursued,  since  the  added 
value  is  secured  only  as  the  result  of  the  operations  of  the 
utility  buying  it. 

Reproduction  Method  Employed  on  Lehigh  Valley  Railroad 

Although  the  reproduction-cost  theory  for  land  has  not 
been  accepted  by  the  Supreme  Court  of  the  United  States, 
it  has  served  as  the  basis  for  the  valuation  of  the  Lehigh 
Valley  Railroad  recently  completed  for  the  company.  In 
this  case  three  methods  were  considered:  original  cost; 
basic  cost  with  no  added  cost  for  damages;  and  reproduc- 
tion cost.  Original  cost  was  rejected  as  impossible  because 
of  faulty  records.  Basic  cost,  or  cost  based  on  average 
normal  worth  of  neighboring  tracts,  was  rejected  as  being 
inequitable.  The  reproduction  method  was  adopted  and 
resulted  in  an  addition  of  50%  to  the  basic  value  of  the 
road,  which  was  believed  to  be  a  fair  estimate  of  the  repro- 
duction cost  of  the  road.9 

8  Minnesota  Rate  Cases,  230  U.  S.  352. 

•Engineering  Record,  May  16,  1914,  Vol.  69,  page  555. 


LAND    IN    VALUATIONS  IICj 

Land  Not  "Used  and  Useful" 

Many  public  utility  corporations  own  land  which, 
although  it  may  be  necessary  for  the  future  expansion  of 
the  plant,  is  for  the  present  unnecessary  for  the  service  of 
the  public.  As  a  general  rule  the  courts  refuse  to  include 
the  value  of  such  land  in  the  valuation  of  the  utility's 
assets,  on  the  ground  that  a  fair  rate  should  be  earned  only 
on  the  property  "used  and  useful"  to  the  public.  It  is  evi- 
dent, however,  that  to  follow  such  a  rule  in  letter  rather 
than  as  a  broad  general  principle,  might  lead  to  results  ex- 
actly opposite  those  sought  in  so  limiting  the  earnings  of 
the  company.  Wherever  such  utilities  have  occasion  to 
operate,  particularly  if  they  have  prospects  of  future  ex- 
pansion, land  appreciates  rapidly  in  value;  and  to  throttle 
the  expansive  power  of  the  company  by  making  it  unprofit- 
able to  acquire  additional  land  in  anticipation  of  future 
growth,  may  tend  to  make  rates  higher  when  the  land  is 
ultimately  purchased  from  necessity,  than  if  the  corpora- 
tion had  been  granted  a  greater  degree  of  liberty  at  an 
earlier  period. 

Too  great  freedom  might  lead  to  speculation,  so  that 
in  this  matter  the  attitude  of  the  courts  should  be  one  of 
guarded  leniency,  granting  to  corporations  a  return  on  such 
unused  property  as  will  be  needed  to  meet  estimated  future 
requirements.  On  the  other  hand,  any  income  from  such 
lands  as  are  not  in  the  public's  service  should  serve  as  an 
offset  to  the  amount  of  the  fair  return  on  such  property 
which  the  public  must  pay ;  and  any  profits  made  by  the  sale 
of  any  such  lands  should  be  treated  likewise. 


Part  III — Determining  the  Depreciation  Charge 


CHAPTER    X 

METHODS  OF  DEPRECIATION 

Depreciation  as  Affected  by  the  Point  of  View 

The  chapters  which  follow1  describe  the  various  plans 
that  have  been  and  still  are  advocated  as  valuable  aids  in  the 
determination  of  the  depreciation  charge.  Only  after  hav- 
ing secured  an  understanding  of  the  principles  employed  in 
any  method  can  its  real  significance  be  realized,  and  only 
thus  can  we  place  ourselves  in  a  position  to  pass  a  rational 
criticism  upon  the  different  methods.  For  this  reason  more 
space  has  been  given  to  their  consideration  than  might 
otherwise  have  been  necessary.  The  whole  question  of 
method  has  become  so  confused  in  the  contest  between 
conflicting  views  and  opinions  that  it  merits  the  most  careful 
consideration. 

Oftentimes  obscurity  results  from  inability  to  keep 
definitely  in  mind  the  full  significance  of  the  thing  for  which 
we  are  striving.  The  question  of  depreciation  is  chiefly 
concerned  with  two  things : 

1.  The  determination  of  the  cost  of  maintaining  the  in- 

vestment, which  in  turn  is  dependent  upon — 

2.  The  extent  to  which  the  investment  has  depreciated 

as  the  result  of  wear  and  tear,  or  other  physical 
decay,  or  of  obsolescence  or  inadequacy. 

The  cost  of  maintaining  the  investment  may  in  turn  be 


1  Chapters  XI-XVI. 

120 


METHODS     OF    DEPRECIATION  I2I 

regarded  as  one  of  the  elements  entering  into  the  cost  of  the 
output,  either  service  or  commodity,  along  with  labor,  fuel, 
and  so  on. 

In  valuations  the  question  of  depreciation  is  not  essen- 
tially different,  the  difference  being  one  rather  of  viewpoint 
than  one  which  affects  the  fundamental  problem  itself.  In 
valuations  attention  is  directed  rather  to  the  extent  of  the 
depreciation  at  a  point  in  time,  for  the  purpose  of  deter- 
mining value  at  that  time,  while  from  the  other  standpoint, 
depreciation  over  a  period  is  the  more  important  considera- 
tion. Valuations  are  made,  for  instance,  to  determine 
whether  the  owners  of  the  property  are  securing  an  ade- 
quate return  on  their  property  at  the  time  of  valuation.  This 
is  the  viewpoint  of  the  Public  Service  Commission,  which 
touches  upon  a  corporation's  affairs  only  at  intervals,  and 
somewhat  as  an  external,  supervisory  agent.  From  the 
viewpoint  of  the  company  officials,  on  the  other  hand,  depre- 
ciation is  a  constantly  accruing  expense,  to  be  as  constantly 
refunded  out  of  the  revenues  of  the  business. 


When  the  character  and  extent  of  an  occurrence  is  de- 
termined by  the  operation  of  one  or  more  agencies  or  forces, 
it  is  said  to  be  functioned,  or  dependent,  upon  such  agencies 
or  forces.  As  the  temperature  falls,  a  steel  rail  contracts 
slightly;  therefore  its  length,  within  certain  limits,  is  func- 
tioned upon  the  temperature.  Similarly,  the  accumulations 
of  a  sinking  fund  are  functioned  upon  (1)  the  amount  of  the 
contributions  to  the  fund;  (2)  the  rate  of  interest;  (3)  the 
time  during  which  the  sinking  fund  accumulates;  (4)  the 
frequency  with  which  interest  is  compounded.  Likewise, 
the  extent  to  which  an  investment  in  an  industrial  plant 
depreciates  is  functioned  upon  (1)  the  wear  and  tear;  (2) 
obsolescence,  arising  from  the  possibility  of  displacement; 


I22  PRINCIPLES     OF    DEPRECIATION 

(3)  inadequacy  to  perform  its  work,  etc.  Depreciation  is  not 
functioned  upon  passage  of  time  but  is  merely  conveniently 
measured  in  terms  of  time.  Thus  we  say  that  in  5  years  a 
plant  depreciates  20%  of  its  cost  price.  We  use  periods  of 
time  as  a  convenient  way  of  comparing  the  rapidity  of 
depreciation  with  the  rapidity  with  which  other  occurrences 
coming  within  our  experience  take  place.  Without  the 
action  of  such  agents  as  wear  and  tear,  obsolescence,  or  in- 
adequacy, the  investment  would  not  depreciate  at  all. 

Great  Accuracy  Impossible 

The  effects  of  past  wear  and  tear,  obsolescence,  and  in- 
adequacy can  be  ascertained  within  reasonably  narrow 
limits.  The  future  effects  of  wear  and  tear,  although  they 
cannot  be  anticipated  with  entire  certainty,  may  also  be 
estimated,  from  experience,  with  a  reasonable  degree  of  cer- 
tainty. Oftentimes  even  inadequacy  may  be  foreseen, 
though  usually  with  a  smaller  degree  of  certainty  than  wear 
and  tear,  because  it  is  sometimes  functioned  upon  unfore- 
seen changes,  such  as  movements  of  population,  changes  in 
demand,  etc.  Obsolescence  can  be  predicted  with  perhaps 
even  less  certainty.  It  is  notable,  however,  that  although 
individual  occurrences  of  a  given  character  transpire  appar- 
ently with  entire  uncertainty  as  to  time,  when  large  num- 
bers of  such  occurrences  are  studied  they  may  be  found  to 
follow  a  law.  Thus  the  length  of  an  individual  life  is  alto- 
gether uncertain.  Yet  when  considered  in  large  numbers  it 
is  discovered  that  the  span  of  the  average  life  is  calculable 
with  enough  accuracy  to  serve  as  a  basis  for  the  science  of 
life  insurance. 

Much  of  the  same  thing  is  true  of  the  items  that  compose 
an  industrial  plant,  although  it  might  not  be  profitable  to 
carry  the  analogy  too  far.  Mortality  tables  of  structures 
have  been  used,  and  still  greater  accuracy  may  be  expected 


METHODS     OF    DEPRECIATION 

as  the  result  of  longer  experience.  It  will  therefore  be  pos- 
sible to  gauge  physical  decay  with  reasonable  accuracy,  while 
obsolescence  and  inadequacy  may  be  covered  by  a  reason- 
able allowance  in  the  nature  of  insurance  over  and  above 
that  for  physical  depreciation,  or  by  being  met  when  the 
exigency  occurs,  by  writing  off  extraordinary  losses,  due  to 
such  causes,  over  a  brief  period  of  years.  The  necessity  of 
this  is  apparent,  for  unless  the  investment  indicated  on  the 
books  is  reduced  to  correspond  to  actual  reductions  in  values 
through  obsolescence  or  inadequacy,  it  will  be  impossible  to 
meet  the  competition  of  more  efficient  plants  and  continue 
paying  a  normal  rate  of  dividends. 

The  Straight  Line  Method 

The  simplicity  of  this  method  of  determining  deprecia- 
tion (Chapter  XI)  stamps  it  with  the  appearance  of  prac- 
ticability. It  is  free  from  interest  complications,  and  its 
employment  does  not  require  a  knowledge  of  the  logarithmic 
or  any  other  method  of  finding  roots  and  powers  of  num- 
bers. Speaking  generally,  there  appears  to  be  no  reason  why 
the  straight  line  method  does  not  approximate  actual  depre- 
ciation as  nearly  as  any  of  the  complicated  curves  at  times 
advocated,  apparently  on  the  assumption  that  actual  depre- 
ciation finds  a  counterpart  in  the  accuracy  of  their  mathe- 
matical computations. 

It  is  not  meant,  however,  to  recommend  unconditionally 
the  straight  line  method.  The  question  is  one  of  expediency 
rather  than  accuracy ;  of  expediency  based  on  the  principle 
that  the  interest  of  stockholders,  bondholders,  and  the  pub- 
lic must  be  diligently  protected.  To  do  this  the  procedure 
adopted  should  guarantee  the  return  to  the  business  through 
the  rates  charged,  of  an  amount  approximately  equal  to  the 
expiration  of  plant  values  incident  to  the  production  of  the 
commodity  or  service  sold.  It  is  axiomatic  that  deprecia- 


124 


PRINCIPLES    OF    DEPRECIATION 


tion  is  one  of  the  costs  of  production,  and  hence  a  corre- 
sponding amount  should  be  charged  to  gross  income,  and 
thus  be  retained  to  offset  the  exhaustion  of  capital. 

The  Reducing  Balance  Method 

This  method  (Chapter  XII)  possesses  the  advantage  of 
freedom  from  interest  calculations,  but,  like  any  other 
method  based  on  a  fixed  procedure,  does  not  take  into  ac- 
count either  the  actual  rapidity  with  which  depreciation 
occurs,  or  the  various  modifying  factors  which  may  show 
their  influence  at  any  time.  Since  this  objection  is  common 
to  all  methods,  other  considerations  will  probably  lead  to  a 
choice.  Emergencies,  such  as  rapid  obsolescence,  can  in  no 
case  be  foreseen ;  and  the  best  that  can  be  done  is  to  alter 
the  basis  upon  which  future  depreciation  allowances  are 
computed,  changing  the  figures  indicating  value  and  remain- 
ing lifetime  to  conform  to  the  altered  conditions. 

A  glance  at  the  table  and  Form  6  in  Chapter  XII  shows 
what  a  preponderance  the  reductions  for  the  first  few  years, 
for  a  property  having  a  lifetime  of  25  years,  bear  to  those 
of  later  years.  Such  a  rate  of  reduction  must  usually  be 
out  of  all  proportion  to  the  actual  rate  of  depreciation  of  the 
units  of  which  an  industrial  plant  is  composed.  From  one 
point  of  view  this  is  the  method  of  extreme  conservatism, 
since  it  writes  down  plant  values  far  more  rapidly  than  any 
other,  and  removes  almost  any  possibility  of  a  failure  to  set 
up  adequate  reserves.  Usually  the  net  result  will  be  the 
formation  of  a  secret  reserve  through  the  undervaluation  of 
assets.  Even  if  we  assume  the  desirability  of  such  a  pro- 
cedure, it  may  be  questioned  whether  a  new  plant  could  bear 
the  burden  of  the  resulting  heavy  charges  to  revenue. 

In  an  old  plant  the  effects  of  the  application  of  this 
method  to  many  units  of  property  of  various  values,  life- 
times, and  conditions,  will  tend  to  give  a  result  of  greater 


METHODS     OF    DEPRECIATION  I2c 

jniformity  in  proportion  to  the  extent  and  variety  of  the 
plant ;  tending,  however,  to  create  a  secret  reserve  measured 
by  the  excess  of  the  Actual  value  over  the  book  value  of  the 
assets.  It  might  be  used  to  advantage  in  certain  instances 
where  obsolescence  or  inadequacy  rapidly  encroaches  upon 
the  property,  although  the  accuracy  with  which  actual  depre- 
ciation would  be  covered  would  be  at  best  approximate,  and 
not  gauged  by  the  extreme  accuracy  with  which  the  percen- 
tage on  the  reducing  balance  is  calculated  from  the  formula. 

Interest 

The  interest  question  in  depreciation  has  a  twofold 
aspect.  On  the  one  hand,  it  has  been  asserted  that  the  actual 
cost  of  an  investment -is  not  merely  the  bare  original  invest- 
ment itself,  but  an  additional  amount  represented  by  interest 
on  the  investment,  since  the  money  thus  invested  might  have 
been  loaned  out  on  security  at  a  fair  rate  of  interest.  This 
theory  has  given  rise  to  the  so-called  "Annuity  Method" 
described  in  Chapter  XIV. 

On  the  other  hand,  interest  has  been  brought',  into  the 
discussion  of  depreciation  in  connection  with  the  establish- 
ment of  sinking  funds  for  the  replacement  of  depreciated 
industrial  plant.  The  "Sinking  Fund"  plan  (Chapter  XIII), 
and  those  which  are  based  upon  the  sinking  fund  principle, 
viz.,  the  "Equal  Annual  Payment"  (Chapter  XV)  and  the 
"Unit  Cost"  (Chapter  XVI)  plans,  require  interest  calcula- 
tions of  this  character. 

The  Sinking  Fund  Method 

The  persistence  with  which  the  sinking  fund  method  has 
been  advocated  makes  a  careful  consideration  of  it  necessary. 
It  is  fully  described  and  illustrated  in  Chapter  XIII.  The 
sinking  fund  formula  provides  a  mathematically  accurate 
method  of  accumulating  a  certain  sum  of  money  in  a  given 


I26  PRINCIPLES    OF    DEPRECIATION 

time  by  means  of  equal  periodic  contributions  permitted  to 
accumulate  at  compound  interest.  Since  such  a  fund  grows 
not  merely  by  the  equal  annual  or  other  periodic  additions 
made  to  it,  but  also  by  the  interest  accumulations  of  these 
additions,  it  follows  that  as  the  time  during  which  the  sink- 
ing fund  accumulates  is  longer  or  shorter,  so  the  portion  of 
the  entire  fund  formed  exclusively  by  interest  accretions  will 
be  larger  or  smaller.  Thus,  a  fund  of  $100  accumulated  in 
25  years,  interest  at  5%  by  equal  annual  contributions,  is 
composed  of  $47.62  interest  accumulations  and  $52.38  direct 
contributions  to  the  fund.  For  a  shorter  period  the  total 
interest  accumulation  would  be  less,  and  for  a  longer  period 
greater,  than  that  given  above. 

From  this,  one  might  conclude  that  the  cost  of  creating  a 
fund  grows  smaller  with  the  increase  in  the  number  of 
years,  since  the  total  contributions  necessary  to  secure  a 
fund  of  $100  in  25  years  on  a  5%  basis  is  only  $52.38,  while 
for  longer  periods  it  is  yet  smaller.  The  fallacy  of  this 
supposition  is  evident,  however,  if  we  remember  that  the 
equal  periodic  contributions  to  the  fund  are  altogether  with- 
drawn from  the  business,  where  they  would  have  been  em- 
ployed at  a  profit,  and  that  the  longer  such  sums  are  held 
impounded  in  the  fund,  the  longer  the  business  is  deprived 
of  their  use.  Indeed,  the  business  is  not  a  very  flourishing 
one  if  it  cannot  earn  more  by  retaining  these  amounts  in  the 
business  than  can  be  secured  in  the  form  of  interest  accre- 
tions to  them  in  a  sinking  fund. 

The  interest  accumulations  of  a  given  year  must  be 
added  to  the  annual  contribution  to  the  fund,  to  discover  the 
actual  burden  for  that  year.  Since  the  interest  accumula- 
tions progressively  increase,  as  may  be  seen  by  a  glance  at 
the  table  in  Chapter  XIII,  the  actual  burden  of  the  fund  also 
increases  yearly.  In  the  foregoing  illustration,  it  is  more 
than  three  times  greater  in  the  last  than  in  the  first  year. 


METHODS     OF    DEPRECIATION 


127 


There  is  no  reason  to  suppose  that  depreciation  increases 
at  such  a  progressive  rate.  Moveover,  the  money  should  in 
most  cases  be  reinvested  in  the  business  where  it  can  be  most 
profitably  employed.  The  considerations  which  will  make 
this  plan  the  advisable  one  to  follow  must  be  such  as  are  not 
usually  confronted  in  practice.  The  seemingly  great  accu- 
racy with  which  the  calculations  can  be  made,  ought  not  to 
blind  us  to  the  essential  phases  of  the  plan. 

Interest  on  Investment — Annuity  Method 

At  first  thought  there  appears  to  be  some  reason  for 
including  an  allowance  for  interest  on  the  depreciated  in- 
vestment, since  the  money  thus  invested  would  ordinarily 
produce  an  income  when  loaned  on  security,  and  without  the 
risks  incident  to  the  investment.  In  reality,  however,  the 
net  profits  of  business  are  usually  composed  of  two  parts  not 
readily  distinguished:  (1)  interest  on  the  investment  at  say 
2  or  2y^%,  about  the  rate  paid  on  gilt-edge  government 
bonds;  and  (2)  over  and  above  this,  a  reward  for  the  extra 
hazards  and  risks  of  the  business. 

Briefly,  a  portion  of  the  net  profits  represents  interest  on 
investment,  and  it  would  be  a  duplication  of  the  interest 
charge  to  include  it  in  the  depreciation  allowance.  An 
inspection  of  the  table  in  Chapter  XIV  will  show  that  the 
total  amount  charged  in  the  case  of  a  $100  property  with  a 
lifetime  of  25  years  is  $177.38,  being  made  up  of  25 
equal  annual  charges  of  $7.0952.  This  is  nearly  twice  the 
amount  of  the  original  investment,  and  the  continued 
reservation  of  amounts  on  this  basis  would  return  not  only 
the  capital  invested  but  a  large  additional  amount,  its  magni- 
tude depending  on  the  interest  rate  and  the  lifetime  of  the 
property.  This  is  equivalent  to  an  actual  reservation  of 
profits,  which,  as  is  shown  in  Chapter  IV.  is  not  the  purpose 
of  the  depreciation  allowance. 


I2g  PRINCIPLES    OF    DEPRECIATION 

There  is  yet  another  objection  to  this  method.  As  the 
reader  will  see  by  an  inspection  of  the  table  in  Chapter  XIV, 
and  of  Form  8,  the  equal  annual  charges  are  composed  of 
both  interest  and  depreciation  charges,  the  depreciation 
charge  increasing  with,  and  being  dependent  upon,  the  de- 
creasing interest  charge.  The  depreciation  charge  is  thus 
made  the  function  of  an  assumed  rate  of  interest,  with  the 
result  that,  in  the  case  of  the  $100  property  with  a  lifetime 
of  25  years,  the  charge  for  depreciation  in  the  25th  year  is 
$6.76  as  contrasted  with  $2.10  in  the  first  year.  There 
would  appear  to  be  no  reason  whatever  for  such  a  proce- 
dure, for  the  property  would,  in  theory,  not  only  be  required 
to  pay  a  return  on  the  remaining  investment  as  at  the  begin- 
ning of  the  25th  year,  amounting  to  $6.76,  but  in  addition 
earn  a  sufficient  amount  during  the  year  to  amortize  its 
entire  value. 

When  one  invests  money  in  an  industrial  plant  he  ex- 
pects a  return  equal  to  the  ordinary  rate,  of  interest  plus  a 
reward  for  entrepreneur's  profit,  risk,  etc.  If  money  can  be 
loaned  on  good  security  for  5%,  by  investing  it  in  business 
one  expects  a  return  to  cover  not  only  interest  which  he 
might  have  received,  but  also  an  additional  percentage  for 
his  extra  labor  and  risk. 

Should  interest  on  investment  be  included  in  the  depre- 
ciation charge,  the  balance  of  the  revenue  account  will  be 
correspondingly,  reduced,  representing  the  gain  over  and 
above  interest,  or  what  may  be  termed  extra-interest  re- 
turns. If  the; money  invested  has  been  borrowed,  and  the 
same  rate  is  allowed  in  the  depreciation  charge  for  interest 
as  is  paid  on  the  money  borrowed,  then,  providing  the  loan 
could  be  paid  off  as  fast  as  the  investment  is  reduced,  the 
total  charge  for  depreciation  and  interest  on  investment 
would  be  just  sufficient  to  pay  the  loan  and  the  interest 
thereon.  Interest  on  borrowed  money  is  a  legitimate  ex- 


METHODS     OF    DEPRECIATION 


129 


pense,  but  it  should  be  considered  under  the  head  of  interest, 
not  of  depreciation. 

In  a  public  utility  whose  rates  are  controlled  by  a  com- 
mission, these  rates  are  fixed  to  afford  a  suitable  income; 
and  since  the  investor  cannot  both  loan  his  money  on  secur- 
ity and  at  the  same  time  invest  it  in  stocks,  the  most  he  can 
ask  is  a  return  equivalent  to  the  ordinary  interest  rate,  plus 
reward  for  hazard,  etc.  Therefore,  if  a  deduction  from 
income  is  made  for  interest  on  investment,  rates  cannot  be 
raised  to  provide  it  again  in  the  profits.  If  an  allowance  for 
interest  on  investment  is  made  in  the  depreciation  charge,  it 
amounts  to  the  retention  of  a  portion  of  the  profits  in  the 
business  without  recognizing  them  as  such. 

The  Equal  Annual  Payment  Method 

Although  an  actual  sinking  fund  is  not  created,  this 
method  employs  the  principles  of  the  sinking  fund  to  deter- 
mine the  depreciation  charge,  by  making  it  what  the  charge 
for  a  sinking  fund  would  amount  to  for  the  period  in  ques- 
tion, plus  a  sum  representing  interest  on  the  remaining 
investment.  This  may  be  seen  by  examining  the  table  in 
Chapter  XV  and  comparing  its  contents  with  those  of  the 
table  in  Chapter-  XIII.  The  result  is  that  if  the  rate  of  in- 
terest on  the  imaginary  sinking  fund  is  the  same  as  that  on 
the  investment,  an  equal  annual  charge  is  secured  exactly 
the  same  as  that  obtained  by  the  annuity  method,  as  indi- 
cated in  column  6  of  the  equal  annual  payment  table,  Chapter 
XV,  and  column  5  of  the  annuity  table,  Chapter  XIV. 
Moreover,  since  the  sinking  fund  is  entirely  imaginary, 
there  appears  to  be  no  objection  to  assuming  the  same  rate 
of  interest  in  both  cases.  When  the  interest  rate  on  invest- 
ment and  in  the  imaginary  sinking  fund  are  the  same,  the 
net  result  of  this  plan  in  the  illustration  given  is  an  exces- 
sive charge  of  $77.38,  representing  interest  on  investment 


PRINCIPLES    OF    DEPRECIATION 

If  the  interest  on  investment  is  placed,at  1%  instead  of  5%, 
it  amounts  to  $208.33  for  an  investment  of  $100,  with  a  life- 
time of  25  years — more  than  double  the  proper  charge. 

Instead  of  bringing  the  depreciation  charge  into  as  close 
correspondence  as  possible  with  the  actual  reduction  of  plant 
values,  it  is  made  a  function  of  the  growth  of  a  sinking  fund, 
and  an  imaginary  one  at  that,  based  on  an  assumed  rate  of 
interest ;  and  in  order  to  make  the  charges  equal  they  are  in- 
creased by  an  imaginary  return  on  the  remaining  invest- 
ment, with  the  result  that  the  equal  annual  charges  are  out 
of  all  proportion  to  the  actual  expiration  of  plant  value.  By 
carrying  the  items  to  the  third  or  fourth  decimal  point,  an 
appearance  of  great  accuracy  is  obtained,  which  in  reality 
bears  little  or  no  relation  to  the  conditions  to  which  it  is 
intended  to  conform. 

Undoubtedly  it  would  be  better  to  write  down  plant 
value  by  the  sinking  fund  method  than  to  make  no  provision 
whatever  for  depreciation.  But  we  must  remember  that  any 
depreciation  charge  based  on  purely  assumed  grounds  may 
be  considerably  at  variance  from  the  actual  conditions. 

The  Unit  Cost  Method 

For  valuations,  especially  where  there  exists  obsolescence 
or  inadequacy,  this  plan,  as  advocated,  contains  much  that  is 
suggestive,  although  vitiated  by  the  introduction  of  the  sink- 
ing fund  principle.  It  is  based  on  the  fallacy  that  the  sum 
of  the  annuities  necessary  to  amortize  plant  value  constitutes 
the  total  cost  of  amortization,  and,  in  so  doing,  underesti- 
mates such  cost  by  the  amount  of  the  interest  accretions  to 
the  sinking  fund.  Since  the  interest  accumulations  form  a 
smaller  proportional  part  of  short-time  funds  than  of  long- 
time funds,  the  net  result  of  the  unit  cost  formula  is  to 
underrate  the  value  of  the  old  plant,  for  in  equation  (3), 
Chapter  XVI, 


METHODS     OF     DEPRECIATION 
Q+P  +  F  +  iV       q  +  p  +  f  +  i 


in  which  F  represents  the  annuity  to  a  sinking  fund  neces- 
sary to  amortize  V,  the  cost  of  the  new  plant,  in  N  years, 
while  f  represents  the  annuity  to  a  sinking  fund  necessary 
to  amortize  v,  the  depreciated  value  of  the  old  plant,  during 
its  remaining  life  of  n  years.  The  left-hand  term  of  the 
equation  is  assumed  to  represent  the  average  unit  cost  of  the 
product,  or  service,  of  the  new  plant;  while  the  right  side 
of  the  equation  is  assumed  to  represent  the  average  unit 
cost  of  the  product,  or  service,  of  the  old  depreciated  plant. 
This  is  true  in  neither  case,  however,  because  F  and  f,  the 
respective  sinking  fund  annuities,  represent  less  than  the 
actual  -burden  of  the  sinking  fund,  as  has  been  shown  ;  but 
since  the  lifetime  of  the  old  plant  is  usually  less  than  that  of 
the  new  one,  the  tendency  is  to  understate  the  real  cost  of 
the  burden  of  the  new  plant  more  than  that  of  the  old  one, 
because  the  annuity  constitutes  a  smaller  part  of  the  burden 
of  a  sinking  fund  over  long  periods  than  over  short  periods. 

Thus,  an  annuity  of  $2.0952  will  accumulate,  at  an  interest 
rate  of  6%,  to  $100  in  25  years  ;  but  $2.0952  X  25  =  $52.38, 
only  a  little  more  than  one-half  of  the  entire  accumulation. 
On  the  other  hand  an  annuity  of  $18.097  will  in  5  years,  at 
5%,  accumulate  to  $100,  while  the  sum  of  the  annual  con- 
tributions will  constitute  far  more  than  52.38%  of  the  total, 
or  $18.097  X  5,  which  amounts  to  $90.485. 

Each  year's  annuity  to  the  25-year  sinking  fund  repre- 
sents but  little  more  than  one-half  of  the  average  burden  of 
the  fund;  while  each  year's  annuity  to  the  5-year  fund  rep- 
resents over  90%  of  the  average  annual  burden  of  the 
annuity.  The  consequence  is  that,  although  cost  of  produc- 
tion is  understated  in  both  cases,  it  is  understated  to  a 
greater  degree  in  the  case  of  a  new  plant  than  in  that  of  a 


132 


PRINCIPLES     OF    DEPRECIATION 


depreciated  one.     The  net  result,  in  the  use  of  the  formula 
given,  is  to  understate  the  value  of  the  old  plant. 

Actual  Depreciation 

In  the  illustrations  of  the  different  methods  of  deprecia- 
tion in  the  following  chapters,  hypothetical  cases  have  been 
assumed,  in  which  plant  value  undergoes  a  gradual  reduc- 
tion from  100%  to  salvage  value,  or  zero.  However,  in 
reality,  an  industrial  plant,  as  a  whole,  does  not  depreciate 
in  this  way.  In  an  extensive  plant,  value  remains  fairly 
fixed,  beyond  a  certain  unavoidable  diminution  during  the 
first  decade  or  so  of  its  existence,  resulting  from  the  aging 
of  the  plant  as  a  whole.  This  general  aging  is  termed 
composite  depreciation,  and  it  amounts  to  possibly  15  or 
20%  of  total  value,  neglecting  improvements.  After  a  cer- 
tain point  has  been  reached,  however,  depreciation  and  re- 
placement become  fairly  complementary.  Only  in  case  of  the 
replacement  of  an  extraordinarily  costly  asset  would  its 
cost  create  an  excessive  burden  on  the  revenues.  In  a  less 
extensive  plant,  or  one  composed  of  a  few  very  expensive 
properties,  replacement  burden,  unless  properly  provided  for, 
might  at  times  be  excessive,  and  even  disastrously  so,  and  a 
method  of  caring  for  such  costs  should  be  contrived  which  is 
sufficiently  simple  to  be  workable  and  at  the  same  time 
accurate  and  inclusive  enough  to  be  valuable. 

Such  a  method  should  not  be  based  upon  the  cost  and 
estimated  lifetime  of  the  entire  plant,  as  this  would  make 
it  impossible  to  give  due  weight  to  variations  in  the  different 
units  composing  the  plant.  Average  lifetime  of  a  plant  is 
too. indefinite  a  basis,  and  makes  impossible  the  proper  allo- 
cation of  the  depreciation  cost  to  the  output  of  the  machine 
or  unit  of  the  plant  to  which  it  is  incident.  In  so  far  as 
any  of  the  formal  methods  described  in  the  following  chap- 
ters are  to  be  advocated,  it  should  be  understood  that  it  is 


METHODS     OF    DEPRECIATION 

only  as  they  apply  to  the  units  into  which  the  plant  can  be 
divided  most  readily,  and  not  to  the  plant  as  a  whole,  which 
is  too  complex  to  serve  as  a  suitable  base  for  calculating 
depreciation. 


CHAPTER    XI 

THE    STRAIGHT   LINE   METHOD 

Characteristics 

This  is  the  simplest  of  the  several  plans  that  have  been 
suggested  to  determine  theoretical  depreciation  and  make 
proper  allowance  for  it  in  the  records.  It  is  based  on  the 
assumption  that  if  the  investment  in  dollars  and  cents  is 
divided  by  the  number  of  years,  or  periods,  of  the  lifetime  of 
a  property,  the  resulting  quotient  expresses  the  amount  in 
dollars  and  cents  which  should  be  allowed  each  year  to  cover 
accrued  depreciation  and  prevent  the  lessening  of  invested 
capital.  Whether  the  best  method  or  not,  it  is  at  once  the 
least  complicated  and  most  easily  understood.  No  interest 
computations  of  any  kind  are  involved,  either  on  the  invest- 
ment itself,  as  in  the  annuity  and  equal  annual  payment 
methods,  or  on  the  annual  allowances,  as  in  the  sinking 
fund  method. 

The  Straight  Line  Formula 

Having  given  the  investment,  lifetime,  and  salvage 
value  of  a  property,  let  V  represent  the  investment;  n  the 
lifetime  in  periods,  as  years  or  months;  and  V*~  the  salvage 
value.  Then  if  we  assume  x  to  equal  the  amount  of  the 
equal  annual  charges,  an  equation  may  be  formed  as  follows : 

V  —  V1 
(1)  *  =  - 

n 

If  salvage  value  is  zero,  then : 

134 


THE    STRAIGHT    LINE    METHOD 


(2)  X  = 

•  n 


Illustration  of  Straight  Line  Method 

Assume  the  case  of  a  plant  costing  $100,  having  a  life- 
time of  25  years  and  a  salvage  value  of  zero.  Substituting 
these  values  in  formula  (2),  we  have: 


$100 


Four  dollars,  therefore,  is  the  annual  charge  necessary 
to  write  off  the  investment  in  25  years. 

Straight  Line  Tabulations 

The  accompanying  table  shows  in  detail  the  accumula- 
tions of  the  charges  when  made  on  this  basis,  and  also  the 
reduced  theoretical  value  of  the  remaining  investment  at  the 
end  of  each  year.  It  is  so  simple  as  to  require  no  explana- 
tion, and  is  given  partly  to  make  the  treatment  uniform 
with  that  in  the  chapters  which  follow. 

Graphic  Illustration  of  Straight  Line  Method 

Form  5  (see  page  137)  is  a  graphic  illustration  of  the 
straight  line  method.  The  upward  progress  of  the  graph 
indicates  value  in  dollars,  while  its  progress  from  left  to 
right  represents  time  in  years.  Thus,  at  the  end  of  the  10th 
year  $40,  or  40%  of  the  investment,  has  in  theory  expired, 
and  has  been  charged  off  in  the  income  account  as  an 
expense. 


136 


PRINCIPLES    OF    DEPRECIATION 

STRAIGHT  LINE  METHOD 
TABLE  OF  COMPUTATIONS 


Age  in                Value  at 
Years         End  of  Each  Year 

Depreciation 
During  Year 

Total  Accrued 
Depreciation  at 
End  of  Each  Year 

0 
1 

$100.00 
96.00 

$4.00 

$4.00 

4.00 

8.00 

2 

92.00 

3 

88.00 

4.00 

12.00 

4.00 

16.00 

4 

84.00 

5 

80.00 

4.00 

20.00 

6 

76.00 

4.00 

24.00 

7 

72.00 

4.00 

28.00 

4.00 

32.00 

8 

68.00 

4.00 

36.00 

9 

64.00 

10 

60.00 

4.00 

40.00 

4.00 

44.00 

11 

56.00 

4.00 

48.00 

12 

52.00 

13 

48.00 

4.00 

52.00 

14 

44.00 

4.00 

56.00 

15 

40.00 

4.00 

60.00 

16 

36.00 

4.00 

64.00 

17 

18 

32.00 
28.00 

4.00 
4.00 

68.00 
72.00 

19 

24.00 

4.00 

76.00 

4.00 

80.00 

20 

20.00 

21 

16.00 

4.00 

84.00 

22 

12.00 

4.00 

88.00 

4.00 

92.00 

23 

8.00 

24 

4.00 

4.00 

96.00 

25 

0.00 

4.00 

100.00 

$100.00 


THE    STRAIGHT    LINE    METHOD 

O        o>  <O  S 


137 


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CHAPTER    XII 

THE  REDUCING  BALANCE  METHOD 

Characteristics 

Assuming  the  plant  to  be  a  unit  which  depreciates  from 
100%  value  to  salvage  value,  the  reducing  balance  method 
requires  heavy  charges  during  the  first  years  of  the  plant's 
lifetime,  these  charges  continually  decreasing  in  amount 
from  year  to  year.  Since  repairs  and  renewals  cost  least 
during  the  first  years,  increasing  with  more  advanced  years, 
they  offset,  to  a  certain  extent  at  least,  this  inequality  of 
charges,  and  tend  to  make  the  total  cost  of  up-keep  and 
depreciation  more  uniform  than  would  otherwise  be  the 
case.  If  it  were  desirable  to  amortize  a  portion  of  the  capi- 
tal as  the  result  of  composite  depreciation,  by  buying  in  part 
of  the  stock,  and  there  were  no  legal  obstacle  in  the  way, 
funds  accumulated  as  the  result  of  the  establishment  of  a 
reserve  larger  than  necessary  for  replacements  could  be 
employed  for  that  purpose.  Or  such  funds,  might  be  used 
for  the  purchase  of  additional  plant  to  compensate  for  com- 
posite depreciation  in  other  portions  of  the  plant.  The 
undetermined  financial  status  of  newly  established  concerns 
sometimes  affords  cause  for  objection  to  this  procedure, 
since,  as  sometimes  unfortunately  occurs,  expediency  may 
compel  the  payment  of  dividends  to  the  sacrifice  of  the 
reserves.  Theoretically,  however,  dividends  cannot  be  paid 
until  depreciation  has  been  allowed ;  so  that  if  the  reducing 
balance  method  is  assumed  to  represent  depreciation,  there 
will  be  no  valid  objection  to  it  on  the  ground  that  it  inter- 
feres with  the  declaration  of  dividends. 

138 


THE    REDUCING    BALANCE    METHOD 

The  Reducing  Balance  Formula 

The  reducing  balance  plan  charges  off  a  constant  per- 
centage on  the  decreasing  balance,  beginning  with  the 
original  investment  and  thus  reducing  it  to  salvage.  This 
constant  percentage  must  be  such  that  at  the  end  of  a 
given  number  of  periods,  or  years,  the  investment  less  sal- 
vage will  have  been  written  off.  A  formula  for  such  a 
procedure  will  now  be  developed. 

Assume  that  V1  represents  salvage  value ;  V  the  original 
investment;  n  the  number  of  periods,  as  years  or  months. 
Let  the  constant  percentage  necessary  to  reduce  V  to  V*  in 
n  periods,  by  deducting  for  each  period  such  percentage 
from  the  balance  remaining  over  from  the  previous  period, 
be  represented  by  x.  Since  V  represents  the  original  value 
of  the  asset,  then,  theoretically,  its  value  at  the  end  of  the 
first  period  will  be  V(\  —  JIT).  To  illustrate,  suppose  we 
know  that  for  a  fixed  number  of  years  the  percentage  by 
which  the  balance  must  each  year  be  reduced  in  order  to 
reach  salvage  value  in  a  stated  number  of  years,  is  37%,  or 
.37  of  the  reducing  balance.  Deducting  .37  of  the  balance 
from  the  reducing  balance  is  equivalent  to  multiplying  the 
balance  by  1  —  .37,  or  .63.  Thus : 

(1)  $100  X. 37  =  $37;  $100  — $37  =  $63 

(2)  $100  X  (1  —  .37)  =$63 

Since  V(\  —  x}  is  the  first  diminished  balance,  result- 
ing from  the  deduction  of  the  fixed  percentage  from  the 
original  investment,  so  V (\. — x~)(\  —  x},  or  V(\  —  x}2  is 
the  diminished  balance  at  the  end  of  the  second  period,  be- 
cause V(\  — x},  the  balance  at  the  beginning  of  the  second 
period,  must  be  reduced  by  the  constant  percentage,  just  as 
was  V,  the  investment  at  the  beginning  of  the  first  year,  by 
multiplying  it  by  (1  — x}.  (1  —  x}  therefore  occurs  twice 


140 


PRINCIPLES     OF    DEPRECIATION 


as  a  multiplier,  i.e.,  it  is  squared,  and  V(l  —  •*•)(!  —  x} 
may  be  stated  better  as  V(1  —  ^r)2.  At  the  end  of  the  third 
period  the  balance  must  again  be  reduced  by  multiplying  by 
(1  —  x),  and  the  resulting  balance  becomes  V(\  —  xY-  If 
n  represents  the  given  number  of  periods,  then  the  balance 
at  the  end  of  the  nth  year  will  be  V  (\  —  x}n,  which,  accord- 
ing to  our  assumption,  must  represent  salvage  value,  or  V1. 
Put  in  form  of  an  equation  : 

(3)  V(\  —  xY=V^ 

We  can  now  find  the  value  of  x,  the  unknown  percen- 
tage, in  terms  of  the  other  quantities,  all  of  which  are 
known.  Dividing  both  terms  of  the  equation  by  V  ,  which 
will  not  alter  the  equality,  we  get  : 


- 

Similarly  we  can  take  the  nth  root  of  both  terms  of 
equation  (4)  without  altering  the  equality,  thus  obtaining: 


(5)  d-^ 

According  to  a  simple  algebraic  principle  the  signs  of 
6oth  terms  of  equation  (5)  may  be  changed  from  +  to  —  or 
from  —  to  +  and  the  equality  still  preserved,  thus : 


nir/i 

(6)  (*-l)=-^ 

Lastly,  the  equality  is  still  preserved  if  in  changing  any 
quantity  from  one  side  of  the  equation  to  the  other  we 
simply  change  its  sign.  Thus  we  may  obtain : 


THE    REDUCING    BALANCE    METHOD 


which  states  the  value  of  x  in  terms  of  time  n,  original 
investment  V,  arid  salvage  F1. 

Illustration  of  Reducing  Balance  Method 

Assume  the  case  of  an  imaginary  plant  costing  $100, 
and  depreciating  in  25  years  to  a  salvage  value  of  $1. 
Further,  assume  that  the  depreciation  occurring  each  year 
is  a  constant  percentage  of  the  balance  of  the  investment 
remaining  at  the  beginning  of  the  year.  The  problem  is  to 
find  this  constant  percentage.  Substituting  our  values  in 
formula  (7)  we  have: 


100 

When  solved  the  value  of  x  is  found  to  be  .168236.     The 
balance  must  therefore  be  reduced  each  year  16.8236%. 

Reducing  Balance  Tabulations 

In  the  table  which  follows  are  tabulated  all  the  items  in 
the  problem,  extending  over  a  period  of  25  years.  The 
first  column  indicates  the  age  of  the  plant;  the  second 
column  the  value  of  the  balance  at  the  end  of  each  year, 
after  having  been  reduced  from  the  previous  year  by 
.168236;  the  third  column  each  year's  depreciation;  while 
the  fourth  column  shows  the  total  accrued  depreciation  to 
the  end  of  each  of  the  1-year  periods.  From  this  it  is  seen 
that  over  50%  has  been  written  off  in  4  years,  and  over 
90%  at  the  end  of  the  13th  year,  or  when  the  plant  has 
barely  passed  middle  age.  The  charges  for  the  last  few 
years  are  insignificant  compared  with  the  first  one. 


142 


PRINCIPLES     OF    DEPRECIATION 

REDUCING  BALANCE  METHOD 
TABLE  OF  COMPUTATIONS 


Age  in 
Years 

The  Reduced 
Balance 

Depreciation 
for  Each  Year 

Amount  of 
Depreciation  from 
Beginning  to  End 
of  Each  Year 

0 

1 

$100.0000 
83.1764 

$16.8236 
13.9933 

$16.8236 
30.8169 

2 

69.1831 

11.6390 

42.4559 

3 

57.5441 

9.6810 

52.1369 

4 

47.8631 

8.0523 

60.1892 

5 

39.8108 

6.6978 

66.8870 

6 

33.1130 

5.5708 

72.4578 

7 

27.5422 

4.6136 

77.0714 

8 

22.9286 

3.8574 

80.9288 

9 

19.0712 

3.2086 

84.1374 

10 

15.8626 

2.6687 

86.8061 

11 

13.1939 

2.2197 

89.0258 

12 

10.9742 

1.8462 

90.8720 

13 

9.1280 

1.5365 

92.4085 

14 

7.5915 

1.2772 

93.6857 

15 

6.3143 

1.0623 

94.7480 

16 

5.2530 

.8835 

95.6315 

17 

4.3685 

.7349 

96.3664 

18 

3.6336 

.6113 

96.9777 

19 

3.0223 

.5084 

97.4861 

20 

2.5139 

.4229 

97.9090 

21 

2.0910 

.3498 

98.2588 

22 

1.7412 

.2929 

98.5517 

23 

1.4483 

.2437 

98.7954 

24 

1.2040 

.2028 

98.9982 

25 

1.0018 

$99.0000 


THE    REDUCING    BALANCE    METHOD 


g 
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- 

bo 

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3 
•O 


PRINCIPLES     OF    DEPRECIATION 

Graphic  Illustration  of  the  Reducing  Balance  Method 

Form  6  indicates  graphically  the  facts  given  in  the  table. 
Vertical  spaces  represent  values,  and  horizontal  spaces  time, 
as  designated.  The  rise  of  the  curve  indicates  the  accrual 
of  depreciation  upon  the  reducing  balance  theory.  In  the 
table,  accrued  depreciation  at  the  end  of  the  6th  year 
amounts  to  $66.89.  This  may  be  found  approximately  in 
the  graph  by  noting  what  amount  in  dollars  is  diagonally 
opposite  the  6-year  point  in  the  rectangle  one  of  whose  up- 
right sides  is  determined  by  the  intersection  of  the  curve 
with  the  vertical  line  drawn  from  6.  The  exact  amount 
in  dollars  is  not  likely  to  be  found,  as  it  is  indicated  at  only 
five  points,  0,  30,  60,  90,  and  100,  each  vertical  space  repre- 
senting $3.  However,  the  amount  indicated  by  the  curve 
for  any  given  time  can  be  read  approximately. 


CHAPTER    XIII 

THE  SINKING  FUND  METHOD 

Characteristics 

The  sinking-  fund  method  derives  its  name  from  the  fact 
that  it  employs  the  principles  which  are  ordinarily  used  in 
the  establishment  of  sinking  funds  for  the  liquidation  of 
bonded  indebtedness,  as  well  as  for  purposes  of  replace- 
ment, etc.  It  might  also  be  called  the  compound  interest 
method,  since  sinking  funds  accumulate  by  compound  in- 
terest, and  because  it  is  sometimes  employed  without  estab- 
lishing an  actual  sinking  fund,  as  in  the  equal  annual 
payment  method,  considered  in  Chapter  XV. 

We  must  not  forget  that  where  the  rate  of  depreciation 
is  made  a  function  of  a  rate  of  interest,  such  depreciation 
is  purely  theoretical,  and  may  or  may  not  approximate 
actual  depreciation.  Some  confusion  has  resulted  from 
attempting  to  indicate  depreciation  by  means  of  interest 
formulas,  with  the  result  that  such  methods  have  been 
branded  by  some  writers  as  illusory,  and  misleading.  The 
way  to  determine  actual  depreciation  is  by  inspection.  But 
this  does  not  necessarily  render  useless,  formulas  which  can 
be  applied  with  due  consideration  of  the  facts  in  the  case. 
The  problem  is  one  of  expediency,  and  whatever  plan  will 
aid  in  a  solution  of  the  problem  ought  to  be  adopted.  Tl:^ 
possible  usefulness  of  the  various  methods  has  already  been 
discusse'd  in  Chapter  X. 

By  the  sinking  fund  method  a  fixed  sum  of  money  is 
placed  aside  each  period  and  allowed  to  accumulate  at  com- 
pound interest.  The  amounts  thus  set  aside,  plus  their  in- 
terest accumulations,  must  be  such  as  to  equal  the  desired 

H5 


146  PRINCIPLES    OF    DEPRECIATION 

amount  at  the  end  of  an  assumed  period.  Although  the 
annual  charges  remain  constant,  the  actual  burden  increases 
each  period,  because  in  addition  to  the  equal  amounts  placed 
in  the  fund  periodically,  there  are  the  continually  increasing 
interest  accumulations  which  represent  the  earning  capacity 
of  the  fund  and  which  are  not  received  through  the  usual 
channels  of  revenue  as  they  would  be  if  the  funds  were  rein- 
vested in  the  business. 

The  Sinking  Fund  Formula 

Assume  an  imaginary  plant  with  a  value  of  $100,  life- 
time of  25  years,  and  salvage  value  of  zero.  Our  problem 
is  to  find  what  sum  of  money  must  be  set  aside  each  year  in 
order  that  at  the  end  of  25  years  the  fund  will  have  accu- 
mulated to  $100,  at  5%  interest,  compounded  annually. 

When  a  series  of  numbers  increases  or  decreases  by  a 
constant  factor,  it  forms  a  geometrical  progression  whose 
terms  consist  of  the  respective  annual  charges  plus  their 
interest  accumulations  at  the  end  of  the  assumed  period  of 
years.  In  the  problem  given,  it  is  evident  that  the  last  one 
of  the  25  fixed  payments  will  accumulate  no  interest,  since 
it  is  made  at  the  end  of  the  25th  year,  when  the  fund  will  be 
needed  to  make  the  desired  replacement.  The  next  to  the 
last  payment  (24th)  will  accumulate  interest  for  1  year; 
while  the  one  preceding  this  will  accumulate  not  only  1 
year's  interest  on  the  payment  made  to  the  fund,  but  also  1 
year's  interest  on  the  sum  of  the  23rd  payment  after  being 
enhanced  by  its  first  year's  interest  accumulation,  and  so  on. 
5%  being  the  rate  of  interest,  we  obtain  a  series  which  in- 
creases by  a  constant  factor  (1.05),  thus: 

The  last  year  the  charge  accumulates  no  interest,  so  it 
amounts  to  1.00  times  the  charge. 

Next  to  last  year  the  charge  accumulates  to  1.05  times 
the  charge. 


THE    SINKING    FUND    METHOD 

Second  year  from  the  last,  the  charge  accumulates  to 
1.1025  (1.05  X  1.05)  times  the  charge. 

Third  year  from  the  last,  the  charge  accumulates  to 
1.157625  (1.1025  X  1.05)  times  the  charge,  and  so  on,  each 
year's  charge  accumulating  to  an  amount  1.05  larger  than 
the  amount  accumulated  by  the  charge  of  the  year 
following. 

Thus  the  constant  factor  is  1.05  in  the  series  consisting 
of  the  annual  charges  plus  their  interest  accretions.  Now, 
if  we  assume  x  to  be  the  fixed  annual  payment  necessary  to 
produce  the  required  sum,  then  x  X  1.05  is  the  accumula- 
tion of  the  next  to  the  last  year's  payment ;  x  X  1.052  that 
of  the  preceding  year;  x  X  1.053  that  of  the  next  preceding; 
and  so  on.  In  this  instance,  x  X  1.0524  is  the  accumulation 
of  the' first  payment  invested.  To  secure  a  general  formula 
let  r  represent  the  constant  factor,  and  n  the  number  of 
years.  Then : 

x  +  xr  +  xrz  -\-  xr*  +  xr*  +  .  .  .  -\- xrn~z  -}- xrn~l 

is  the  general  form  of  the  increasing  geometrical  progres- 
sion. The  sum  of  these  terms,  or  V ,  must  equal  the  fund 
accumulated  after  n  years,  by  investing  x  dollars  in  a  fund 
accumulating  at  the  rate  of  r.  This  sum  is  a  known  quan- 
tity, being  $100  in  the  problem  assumed.  By  a  well-known 
mathematical  principle,1 


(r-1) 
(2)  .vr  "- 


(r-1) 


1  To  find  the  sum  of  the  terms  of  a  geometric  series,  multiply  the  greatest 
term  by  the  ratio;  from  the  product  subtract  the  least  term;  divide  the  remainder 
by  the  ratio  less  1. 


14g  PRINCIPLES    OF    DEPRECIATION 


(r-l) 


Illustration  of  Sinking  Fund  Method 

Substituting  in  equation  (4)  the  values  assumed  above, 
and  solving  by  logarithms,  we  have: 


x  =  $100     Q5,5_1=  $2.0952+ 

That  this  amount  set  aside  each  year,  at  5%  compound 
interest,  for  25  years,  will  amount  to  $100,  may  be  proven 
by  using  formula  (3)  : 


(-1    AK25  -I  \ 

V  =  $2.0952-Vr7^ TT  = 

(l.Oo  —  i) 


Since  in  practice  fractions  smaller  than  one  cent  cannot 
be  dealt  with,  the  amount  of  each  instalment  would  be 
$2.10.  This,  compounded  at  5%  for  25  years,  would 
slightly  exceed  $100,  and  would  amount  to  $100.22. 

Sinking  Fund  Tabulations 

In  the  table  which  follows,  all  figures  secured  in  the 
solution  of  this  problem  are  tabulated.  The  first  column 
shows  the  age  in  years:  the  second  column  the  value  at  the 
end  of  each  year;  the  third  column  the  equal  annual  pay- 
ments to  the  depreciation  fund:  the  fourth  column  the  in- 
terest accumulations  of  the  fund:  and  the  fifth  column  the 


149 


SINKING  FUND  METHOD 
TABLE  OF  COMPUTATIONS 


Age  in 
Years 

Value  at 
End  of 
Year 

Annual  Pay- 
ment to  Sink- 
ing Fund 

Annual  Ac- 
cretion of 
Interest  in 
Sinking  Fund 

Actual  Annual 
Cost,  or  Pay- 
ment, Plus 
Year's  Interest 
Accumulations 

0 
1 

$100.0000 
97.9048 

$2.0952 

$0.0000 

$2.0952 

2 

95.7074 

2.0952 

.1049 

2.2001 

3 

93.3947 

2.0952 

.2148 

2.3100 

4 

90.9693 

2.0952 

.3302 

2.4254 

5 

88.4225 

2.0952 

.4516 

2.5468 

6 

85.7483 

2.0952 

.5790 

2.6742 

7 

82.9405 

2.0952 

.7126 

2.8078 

8 

79.9923 

2.0952 

.8530 

2.9482 

9 

76.9866 

2.0952 

1.0005 

3.0957 

10 

73.6462 

2.0952 

1.1552' 

3.2504 

11 

70.2333 

2.0952 

1.3177 

3.4129 

12 

66.6497 

2.0952 

1.4884 

3.5836 

13 

62.8870 

2.0952 

1.6675 

3.7627 

14 

58.9361 

2.0952 

1.8557 

3.9509 

15 

54.7876 

2.0952 

2.0533 

4.1485 

16 

50.4317 

2.0952 

2.2607 

4.3559 

17 

45.8581 

2.0952 

2.4784 

4.5736 

18 

41.0557 

2.0952 

2.7072 

4.8024 

19 

36.0133 

2.0952 

2.9472 

5.0424 

20 

30.7187 

2.0952 

3.1994 

5.2946 

21  . 

25.1594 

2.0952 

3.4641 

5.5593 

22 

19.3221 

2.0952 

3.7421 

5.8373 

23 

13.1930 

2.0952 

4.0339 

6.1291 

24 

6.7574 

2.0952 

4.3404 

6.4356 

25 

0.0000 

2.0952 

4.6622 

6.7574 

$52.3800       $47.6200     $100.0000 


PRINCIPLES    OF    DEPRECIATION 


(0 


K> 


3 


8 


THE     SINKING    FUND    METHOD 

actual  burden  for  each  year  secured  by  combining  the  results 
in  the  third  and  fourth  columns. 

Graphic  Illustration  of  Sinking  Fund  Method 

The  problem  is  solved  graphically  in  Form  7.  Curve  1 
indicates  the  growth  of  the  interest  accumulations;  2  the 
equal  annual  charges  (this  is  a  straight  line)  ;  and  curve  3 
the  resultant  of  1  and  2.  Note  that  in  this  instance  the 
interest  accumulations,  $47.62,  are  but  slightly  less  than  the 
payments  to  the  fund,  $52.38. 


CHAPTER    XIV 

THE   ANNUITY   METHOD 

Characteristics 

This  method  bears  some  resemblance  to  the  equal  annual 
payment  method  (Chapter  XV),  as  in  both  an  allowance  is 
made  for  interest  on  the  investment  remaining  at  the  begin- 
ning of  each  period.  Under  the  equal  annual  payment 
method  the  diminution  of  the  investment  is  arbitrarily  de- 
termined by  assuming  that  the  depreciation  is  equal  to  the 
gradual  increase  of  a  sinking  fund  based  on  a  given  rate  of 
interest. 

Similarly  the  annuity  method  proceeds  on  the  assump- 
tion that  interest  on  the  remaining  investment  should  be 
allowed  for  in  the  revenues ;  and  also  that  the  annual  allow- 
ances should  be  equal,  as  is  the  case  under  the  equal  annual 
payment  method  when  the  rate  of  interest  on  the  investment 
is  the  same  as  is  assumed  for  the  sinking  fund. 

Under  the  annuity  method,  however,  the  equal  annual 
charge  is  determined  without  the  assumption  of  any 
depreciation  rate,  by  merely  finding  such  a  sum  as,  when 
deducted  each  year  from  the  sum  of  the  remaining  invest- 
ment and  the  interest  thereon  at  a  given  rate,  will  write 
down  the  investment  to  salvage,  or  zero,  and  in  addition 
return  the  full  amount  of  the  interest  on  the  investment  as  it 
stands  from  beginning  to  end  of  the  plant's  life.  Interest 
for  the  first  year  is  on  the  original  investment;  for  the 
second  year  on  the  original  investment  reduced  by  the 
amount  that  the  total  annual  allowance  for  interest  and 
depreciation  is  in  excess  of  the  interest  on  investment  for 
the  first  year.  Thus  that  part  of  the  allowance  covering  the 

152 


THE    ANNUITY    METHOD 

item  of  interest  will  gradually  diminish,  while  that  part 
covering  depreciation  will  correspondingly  increase,  the  two 
combined  being  always  the  same. 

But,  whereas  under  the  equal  annual  payment  method 
the  amount  of  the  depreciation,  and  consequently  the  re- 
maining investment,  depends  upon  the  growth  of  a  theoreti- 
cal sinking  fund,  under  the  annuity  method  the  controlling 
factor  is  the  rate  of  interest  on  the  investment.  As  the  rate 
is  lowered  this  method  approaches  nearer  and  nearer  to  the 
straight  line  method,  becoming  identical  with  it  when  the 
interest  is  zero.  Under  the  equal  annual  payment  method 
the  depreciation  is  made  a  function  of  the  rate  of  interest 
upon  which  a  sinking  fund  accumulates,  while  in  the  an- 
nuity method  the  depreciation  is  a  function  of  the  assumed 
rate  of  interest  on  the  investment. 

The  Annuity  Formula 

The  annuity  plan  charges  off  an  equal  amount  each  year 
sufficient  to  cover  interest  on  the  remaining  investment,  and 
in  addition  to  reduce  plant  to  salvage,  or  zero,  at  the  end  of 
a  given  time.  Let  V  represent  original  value,  V1  salvage 
value,  n  the  lifetime  of  the  plant,  and  r  the  rate  of  interest 
plus  1. 

Since  V  is  the  original  value,  Vr,  that  is,  V  multiplied 
by  1  plus  the  rate  of  interest,  is  the  sum  of  the  original 
investment  plus  interest  on  it  for  the  first  period.  For 
instance,  if  the  original  value  is  $100,  and  interest  on  invest- 
ment is  computed  at  5%,  then  $100  X  1.05  (1  plus  the  rate 
of  interest)  equals  $105,  or  the  original  investment  plus 
one  years  interest. 

If  we  let  x  represent  the  equal  annual  charge,  the 
amount  of  which  we  are  seeking,  and  which  is  just  suffi- 
cient to  return  both  principal  and  interest  thereon  at  the 
given  rate,  then  it  is  clear  that  the  investment  remaining 


PRINCIPLES    OF    DEPRECIATION 

after  the  first  annual  charge — and  the  investment  at  the 
beginning  of  the  second  period — will  be  (Vr —  #).  There- 
fore, following  the  same  procedure  as  before,  the  interest 
on  the  investment  for  the  second  period  will  be  (Vr  —  x} 
multiplied  by  1  plus  the  rate  of  interest,  or  (Vr  —  x}r. 
From  this  in  turn  we  deduct  x,  the  second  annual  charge, 
which  gives  us  the  investment  at  the  beginning  of  the  third 
period,  or  (Vr  —  x*)r —  x,  and  so  on  for  as  many  periods 
as  necessary.  Suppose  the  lifetime  of  the  plant  is  four 
years,  then : 

(1)  {[(Vr  —  x}r  —  x\r  —  x}r  —  x=V* 
Removing  the  first  parentheses, 

(2)  [(Vr  —  x}r  —  x}rz  —  xr  —  x=Vl 

Removing  the  second  parentheses, 

(3)  (Vr  —  x}rz  —  xrz  —  xr  —  x=Vl 

Removing  the  last  parentheses, 

(4)  Vr*  —  xr*  —  xr2  —  xr  —  x  =  V1 

We  next  solve  this  equation  for  x,  by  first  transferring 
Vr*  to  the  opposite  side  of  the  equation,  changing  its  sign, 
thus: 

(5)  —  xr*  —  xr2'  —  xr  —  x  =  V1  —  Vr* 
Changing  the  signs  of  all  terms  we  have : 

( 6 )  xrz  +  xr2  +  xr  +  x  =  Vr*  —  V1 
Or, 

(7)  x(i*  +  r2  +  r  +  1)=  Vr*  —  V1 


THE    ANNUITY    METHOD 
Dividing  both  terms  by  (r3  +  r2  +  r  +  1), 


Or, 

(9) 


(r    -I) 


By  substituting  n  for  4,  a  general  formula  is  obtained, 
applicable  to  any  number  of  periods,  thus  : 


(10)  x=(Vr"—     1      ^r~ 


(rn  -1) 

Illustration  of  Annuity  Method 

Assume  an  imaginary  plant  costing  $100  and  having  a 
lifetime  of  25  years.  Assume  further  that  the  investment 
as  at  the  beginning  of  each  year  should  have  a  return  of  5% 
thereon.  Substituting  these  known  terms  in  our  formula 
we  have : 

*  =  100  X  1.0525 


(1.05a5  — 1) 

which  when  solved  with  the  aid  of  logarithms  gives 
$7.095245+  for  the  value  of  x;  that  is,  the  equal  annual 
allowance  that  must  be  made  to  afford  a  return  of  5%  on 
the  investment,  and  also  reduce  the  investment  to  zero  at 
the  end  of  the  25th  year.  Since  the  investment  gradually 
.decreases,  the  theoretical  depreciation  gradually  increases; 
the  sum  of  interest  on  investment  plus  depreciation  allow- 
ance being  always  $7.095245+.  It  Should  be  noted  that 
the  same  results  arc  secured  by  this  method  as  by  the  equal 
annual  payment  method  when  the  rate  of  interest  employed 


156 


PRINCIPLES     OF    DEPRECIATION 


is  the  same  as  is  used  in  the  equal  annual  payment  method, 
both  for  computing  depreciation  on  a  sinking  fund  basis 
and  for  computing  interest  on  the  investment. 

Annuity  Tabulations 

The  table  which  follows  details  the  computations  for 
the  problem  given  above.  The  first  column  gives  the  age  of 
the  plant  in  years ;  the  second  column  indicates  the  theoreti- 
cal value  at  the  end  of  each  year ;  the  third  column  gives  the 
interest  on  the  remaining  investment  each  year;  the  fourth 
column  gives  the  theoretical  depreciation;  and  the  items  in 
the  fifth  column  are  formed  by  combining  interest  on  in- 
vestment and  depreciation,  which  is  the  allowance  for  each 
year.  The  contents  of  the  accompanying  annuity  table 
should  be  carefully  compared  with  those  of  the  equal  annual 
payment  table  of  Chapter  XV. 

Graphic  Illustration  of  Annuity  Method 

This  problem  is  illustrated  graphically  in  Form  8. 
Curve  1  indicates  the  depreciation ;  curve  2  the  interest  on 
the  investment;  and  the  straight  line  3  shows  the  resultant 
of  curves  1  and  2. 


THE    ANNUITY    METHOD 

ANNUITY  .METHOD 
TABLE,  OF  COMPUTATIONS 


AO-P  in       Value  a<-           Interest  on  Re- 
Age  in       Value  at       maining  Value  of 

\ears    End  of  Year      Prope?tyat5% 

Combined 
Depreciation 
Allowance 

Depreciation 
Plus  Interest 
on  Investment 

0       $100.0000 
1            97.9048 

$5.0000 

$2.0952 

$7.0952 

4.8952 

2.2001 

7.0952 

2 

95.7047 

4.7852 

2.3100 

7.0952 

3 

93.3947 

4.6697 

2.4254 

7.0952 

4 

90.9693 

4.5484 

2.5468 

7.0952 

5 

88.4225 

4.4211 

2.6742 

7.0952 

6 

85.7483 

4.2874 

2.8078 

7.0952 

82.9405 

4.1470 

2.9482 

7.0952 

8 

79.9923 

3.9996 

3.0957 

7.0952 

9 

76.8966 

10 

73.6462 

3.8448 

3.2504 

7.0952 

3.6823 

3.4129 

7.0952 

11 

70.2333 

3.5116 

3.5836 

7.0952 

12 

66.6497 

3.3325 

3.7627 

7.0952 

13 

62.6462 

14 

58.9361 

3.1443 

3.9509 

7.0952 

2.9468 

4.1485 

7.0952 

15 

54.7876 

16 

50.4317 

2.7394 

4.3559 

7.0952 

17 

45.8581 

2.5216 

4.5736 

7.0952 

18 

41.0557 

2.2929 

4.8024 

7.0952 

2.0528 

5.0424 

7.0952 

19 

36.0133 

20 

30.7187 

1.8006 

5.2946 

7.0952 

1.5359 

5.5593 

7.0952 

21 

25.1594 

1.2580 

5.8373 

7.0952 

22     •" 

19.3221 

23 

13.1930 

.9661 

6.1291 

7.0952 

24 

6.7574 

.6596 

6.4356 

7.0952 

.3379 

6.7574 

7.0952 

25 

0.0000 

$77.3800       $100.0000       $177.3800 


158 


PRINCIPLES    OF    DEPRECIATION 


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1  1  1  1  1  Li  1144^1 

CHAPTER    XV 

THE    EQUAL   ANNUAL    PAYMENT    METHOD 

Characteristics 

This  method1  has  been  devised  for  the  purpose  of  se- 
curing an  equalized  depreciation  charge,  and  thus  a  uniform 
investment  cost.  By  investment  cost  is  meant  that  part  of 
the  cost  of  the  output  which  arises  from  the  investment  in 
the  industrial  plant,  without  which  operations  could  not  be 
carried  on.  Investment  cost  will  depend  upon  the  amount 
of  capital  sunk  in  the  enterprise  and  the  rapidity  with  which 
it  is  exhausted.  Thus,  if  a  plant  capable  of  turning  out  one 
thousand  units  of  a  uniform  product  each  year  for  10  years, 
costs  $10,000,  then  the  investment  cost  per  unit  is  $1, 
ignoring  interest.  If  the  $10,000  invested  in  the  plant  is 
worth  6%  interest,  then  the  total  investment  cost  is  $10,000 
plus  the  interest  on  that  amount  for  10  years  at  6%,  or 
$16,000.  This  assumes  that  the  total  investment  remains  in 
the  plant.  If  at  the  end  of  each  year  a  portion  of  the  invest- 
ment is  returned,  as  it  should  be  under  a  proper  system  of 
charging  for  depreciation  or  exhausted  capital  outlay,  the 
interest  charge  on  the  remaining  investment  will  decrease 
each  year  in  proportion  to  the  amount  of  the  investment  so 
amortized,  and  the  interest  plus  the  investment  will  be  con- 
siderably less  than  $16,000. 

In  theory  this  equal  annual  investment  charge  would  be 
secured  when,  taking  into  consideration  the  interest  cost  on 
the  continually  decreasing  investment,  an  equal  annual 
charge  is  made  against  revenue  that  will  cover  both  depre- 


1  Suggested  by  the  Special  Committee  on  Valuation  of  the  American  Society 
of  Civil  Engineers,  in  their  tentative  report  of  Dec.  31,  1913. 

159 


T6o  PRINCIPLES     OF    DEPRECIATION 

ciation  of  the  remaining  investment  and  the  interest  cost 
incident  to  such  investment. 

Assume  the  case  of  a  property  costing  $100,  having  a 
lifetime  of  25  years.  The  money  invested  has  been  bor- 
rowed at  5%  interest.  To  simplify  matters  we  shall  for  the 
present  neglect  salvage  value  and  repairs.  How  can  we 
determine  the  equal  annual  investment  cost  and  therefore 
the  annual  depreciation  charges  to  cover  such  cost,  so  that 
out  of  such  charges  the  investment  can  be  amortized  and 
interest  at  5%  paid  on  the  continually  reducing  investment? 
That  is,  instead  of  waiting  until  the  end  of  the  25th  year 
to  repay  the  loan  of  $100,  a  payment  is  to  be  made  thereon 
each  year  of  a  sum  representing  depreciation  during  the 
year  plus  interest  on  the  investment  as  at  the  beginning  of 
the  year.  The  reduction  of  the  interest  charge  will  depend 
on  the  rapidity  with  which  the  investment  theoretically 
depreciates  and  is  amortized  through  the  annual  charges. 
Since  interest  cost  gradually  diminishes,  it  follows  that  to 
make  the  charge  equal  from  year  to  year  the  depreciation 
must  correspondingly  increase. 

Illustration  of  Equal  Annual  Payment  Method 

The  sum  which  must  be  placed  in  a  sinking  fund  each 
year  so  that  such  annual  payments  plus  their  accumulations 
at  5%  compound  interest  will  amount  in  25  years  to  $100, 
is,  according  to  the  formula  explained  in  Chapter  XIII, 
$2.0952+.  By  the  equal  annual  payment  method,  instead 
of  establishing  a  sinking  fund,  each  annual  depreciation 
charge  is  made  equal  to  what  the  annual  payment  to  a  sink- 
ing fund  plus  the  interest  accumulations  for  that  year  would 
have  amounted  to  had  such  a  fund  been  established.  In  the 
third  column  of  the  table  which  follows,  the  depreciation 
for  each  year  is  assumed  to  be  equal  to  the  annual  increase 
of  a  sinking  fund  into  which  annual  payments  of  $2.0952+ 


THE  EQUAL  ANNUAL  PAYMENT  METHOD   iGi 

are  made  and  allowed  to  accumulate  at  5%  interest,  thus 
amounting  to  $100  at  the  end  of  25  years.  These  amounts, 
when  deducted  from  the  amount  invested  as  at  the  begin- 
ning of  each  year,  give  the  remaining  investment  upon 
which  interest  for  the  next  year  is  computed.  The  return 
on  the  remaining  investment  as  at  the  beginning  of  each 
year  is  shown  in  the  fourth  column  at  5%,  and  in  the  fifth 
column  at  7%.  The  sixth  and  seventh  columns  show  the 
depreciation  and  interest  on  the  remaining  investment  com- 
bined. It  is  only  when  the  same  rate  of  interest  is  assumed 
for  computation  of  the  depreciation  by  the  sinking  fund 
method  and  for  the  interest  on  the  remaining  investment, 
that  the  amount  of  the  two  when  combined  remains  a  con- 
stant quantity. 

Since  a  sinking  fund  is  not  really  established,  the  fol- 
lowing question  arises :  What  is  to  determine  the  rate  of 
interest  to  be  employed  in  making  the  computation  of  the 
depreciation  ?  This  leads  to  a  consideration  of  what  appears 
to  be  the  leading  defect  of  the  method,  viz.,  that  the  amount 
of  the  depreciation,  and  consequently  the  amount  of  the 
remaining  investment,  is  assumed  to  be  dependent  upon  the 
laws  of  compound  interest.  There  is  no  ground  whatever 
for  such  an  assumption,  and  if  property  depreciates  to  the 
same  extent  that  a  sinking  fund  accumulates,  it  is  due 
merely  to  a  coincidence,  and  one  which  it  is  safe  to  say 
never  occurs  in  reality.  This,  however,  does  not  neces- 
sarily negative  the  value  of  the  plan,  which,  it  would  appear, 
might — after  a  careful  comparison  of  the  various  sinking 
fund  carves  with  actual  conditions,  to  find  what  one  most 
nearly  approximates  such  conditions — be  of  much  value  in 
determining  a  uniform  or  nearly  uniform  charge. 

Equal  Annual  Payment  Tabulations 

In  the  table  which  follows  are  given  all  the  tabulations 


162 


PRINCIPLES     OF    DEPRECIATION 


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THE    EQUAL    ANNUAL    PAYMENT    METHOD 


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164 


PRINCIPLES    OF    DEPRECIATION 


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&       $       s 

Form  9.    Curves  Illustrating  Equal  Annual  Payment  Method  (plotted 

from  data  on  pages  162,  163).    The  figures  at  left  of  curves 

indicate  value  in  dollars. 


THE  EQUAL  ANNUAL  PAYMENT  METHOD 

illustrative  of  this  plan  for  an  investment  of  $100,  having  a 
lifetime  of  25  years,  with  depreciation  based  on  a  sinking 
fund  accumulating  at'  5%  compound  interest,  and  returns 
of  5%  and  7%,  respectively,  on  the  remaining  investment. 
The  items  in  the  sixth  column  are  formed  by  combining  the 
items  of  the  third  and  fourth  columns;  while  the  items  in 
the  seventh  column  are  formed  by  combining  the  items  of 
the  third  and  fifth  columns. 

Graphic  Illustration  of  Equal  Annual  Payment  Method 

In  Form  9  these  facts  are  indicated  graphically.  Curve  1 
represents  depreciation;  curve  2  represents  return  on  the 
investment  at  5%  ;  curve  3  represents  return  on  the  invest- 
ment at  7%.  The  straight  line  4  is  the  resultant  of  curves 
1  and  2,  while  curve  5  represents  the  resultant  of  1  and  3. 
Note  that  while  4  is  a  straight  line,  5  is  slightly  curved, 
owing  to  the  slightly  decreasing  charge,  as  shown  in  the 
seventh  column  of  the  table, 


CHAPTER    XVI 

THE  UNIT  COST  METHOD 

Characteristics 

This  is  a  modification  of  the  sinking  fund  method,  based, 
its  advocates  claim,  on  the  proposition  that  decrease  of 
plant  value  is  determined  by  increased  cost  of  service  or  out- 
put, and  may  result  either  from  obsolescence  or  actual  phy- 
sical depletion.  It  is  claimed  by  the  advocates  of  the  unit 
cost  method  that  the  sinking  fund  formula  is  not  of  a  suffi- 
ciently general  type  to  take  into  consideration  all  the  factors 
which  enter  into  the  problem;  as,  for  example,  the  loss  in 
economy  resulting  from  the  use  of  an  old  machine.  The 
unit  cost  method,  it  is  said,  takes  into  consideration  these 
factors,  being  based  on  the  principle  that  the  true  price  of  a 
second-hand  machine  is  such  that  during  its  remaining  life 
the  cost  of  output  will  be  the  same  as  during  the  life  of  a 
new  machine. 

The  Unit  Cost  Formula 

The  unit  cost  formula  is  developed  on  the  basis  of  value 
applicable  to  a  given  depreciated  machine,  and  on  value 
applicable  to  a  new  machine.  That  is,  by  making  a  com- 
parison of  a  worn  and  a  new  plant  on  the  basis  of  known  or 
assumed  facts,  their  relative  values  are  found  to  be  such 
that  a  unit  of  output  will  cost  the  same  for  the  old  as  for  the 
new  machine.  To  accomplish  such  a  result  it  is  necessary 
to  take  into  consideration  the  following  factors:  (1)  the 
cost  of  amortizing  the  new  machine;  (2)  the  depreciated 
value  of  the  old  machine;  (3)  the  average  annual  operating 
expenses,  not  including  repairs,  of  both  machines  for  their 

166 


THE    UNIT.  COST    METHOD 


167 


given  lifetime;  (4)  the  annuities  which  will  be  sufficient  to 
provide  repairs  for  both  machines;  and  (5)  the  number  of 
units  of  output  which- each  machine  is  capable  of  producing. 
These  values,  for  use  in  developing  the  unit  cost  formula, 
may  be  expressed  as  follows : 

V  =  first  cost  of  new  machine. 

v  =  depreciated  value  of  old  machine. 

F  =  sinking  fund  annuity  to  amortize  V  in  its  life  of  N 

years. 
/  =  sinking  fund  annuity  to  amortize  v  in  its  life  of  n 

years. 

N  =  lifetime  in  years  of  new  machine. 
n  =  remaining  lifetime  in  years  of  old  machine. 
Q  =  average  annual  operating  expense  of  new  machine, 

not  including  repairs,  during  N  years. 
q  =  average  annual  operating  expense  of  old  machine, 

not  including  repairs,  during  remaining  lifetime 

of  n  years. 
P  =  annuity  necessary  to  meet  repairs  of  new  machine 

during  N  years. 
p  =  annuity  necessary  to  meet  repairs  of  old  machine 

during  n  years. 
i   =  rate  of  interest. 
U  =  average  cost  per  unit  of  output  of  new  machine  tor 

N  years. 
u  =  average  cost  per  unit  of  output  of  old  machine  for 

n  years. 
Yr=  average  number  of  units  of  output  per  annum  of 

new  machine  during  N  years. 
y  =  average  number  of  units  of  output  per  annum  of 

old  machine  during  n  years. 

The  average  unit  cost  for  the  old  and  new  machines  may 
be  expressed  thus : 


1 68  PRINCIPLES    OF    DEPRECIATION 

O  _|_  p   |    JJ   [    -f/ 

(1)  £/=- 

(2)  w 


Y 
__  g  +  p  +  f  +  iv 


According  to  our  theorem,  the  unit  cost  of  both  old  and 
new  machines  must  be  the  same  ;  therefore  : 

(3)  Q+P  +  F  +  iV        q 


Y  y 

According  to  formula  (4)  in  Chapter  XIII,  the  V  being 
dropped  as  it  here  equals  1,  the  sinking  fund  annuity 
necessary  to  accumulate  $1  in  N  years  is  : 


(4) 


Substituting  (!  +  «')  for  r  we  have 


Similarly  the  sinking  fund  annuity  necessary  to  accumu 
late  $1  in  n  years  is  : 


(6) 


To  accumulate  V  dollars  in  N  years  will  therefore  re- 
quire an  annuity  of: 


<»>. 


THE    UNIT    COST     METHOD 


169 


To  accumulate  v  dollars  in  n  years  will  require  an  an- 
nuity of  : 

iv 

f  =  xv~-~~  — 


These  values  of  F  and  /  may  now  be  substituted  in 
equation  (3),  as  follows: 

(9)          Q  +  P  +  XV  +  iV  ^  g  +  p  +  xv  +  iv 
Y  y 

Equation  (9)  may  now  be  solved  for  v,  the  depreciated 
value  of  the  old  plant.     Multiplying  both  terms  by  y, 


(10) 


Y 


Transferring  (<?  +  />)  to  the  opposite  side  by  changing 
their  sign, 


(11) 


Since  v  is  common  to  both  items  of  the  left-hand  side  of 
the  equation,  it  may  be  written : 

.  Y 

Dividing  both  terms  of  the  equation  by    (x  +  i)    we 
have: 


> 


170  PRINCIPLES     OF    DEPRECIATION 

Or,   extending  the  parentheses  to  include    (<?  +  />)   by 

multiplying1  and  dividing  it  by  -  -  —  (thus  leaving  its 

O  +  0 

value  unchanged),  we  have: 


Y  y 

which  is  the  general  form  of  the  unit  cost  formula.  Values 
of  .Y  and  x  are  calculated  by  the  sinking  fund  formulas  (5) 
and  (6).' 

If  the  annual  number  of  units  of  output  of  the  old  and 
new  machines  are  the  same,  then  Y  —  y  and  equation  (14) 
becomes  : 


v= 


(•*"•" 

Or, 


When  the  average  annual  operating  expenses  of  the  old 
and  new  plants  are  the  same,  Q  =  q  and  the  formula 
becomes  : 


When  Q  +  P  =  q  +  p,  the  formula  becomes 

(18)  v  =     (x  +  i\ 

which  may  be  proven  to  be  but  another  form  of  the  sinking 
fund  formula. 


THE    UNIT    COST     METHOD 

Illustration  of  Unit  Cost  Method 

Let  $100  represent  the  cost  of  a  unit  of  plant,  with  an 
estimated  lifetime  of  25  years,  5  years  of  which  has  expired. 
Let  5%  be  the  rate  of  interest  on  the  investment,  while  the 
average  annual  operating  expense,  excluding  repairs,  is  $50 
a  year.  The  annuity  to  provide  for  repairs  during  the 
remaining  years  is  $12.  When  this  plant  unit  was  pur- 
chased it  was  clearly  worth  its  full  cost.  With  the  passage 
of  time,  however,  improvements  are  made,  so  that  a 
machine  of  equal  durability  may  be  secured  5  years  later  at 
a  cost  of  $100,  which  will  turn  out  an  average  of  40  units 
per  annum,  at  a  reduction  from  $12  to  $11  per  annum  for 
repairs,  and  from  $50  to  $48  for  operating  expense.  In- 
terest on  investment  remains  the  same.  It  is  estimated  that 
the  old  machine  will  turn  out,  on  an  average,  38  units  per 
annum  during  the  rest  of  its  lifetime,  20  years. 

If  now  we  substitute  these  values  in  formula  (14),  we 
have : 


/$48  +  $11  +  $2.0952  +  $5     $50  +  $12\ 
>\  40  38        / 


=  38          /$48  +  $11  +  $2.0952  +  $5     $50  +  $12N 

^".03024 +  .05 


From  this  we  find  the  value  of  v — which  is  the  depreciated 
value  of  the  old  plant — to  be  $9.85. 

The  accuracy  of  the  results  secured  by  this  method  are 
commented  on  in  Chapter  X. 


Appendix 

CHAPTER    XVII 

LOGARITHMS   AND   THEIR   USE 

Computing  Interest 

Interest  computations  extending  over  long  periods,  as 
well  as  other  calculations  involving  extended  processes  of 
multiplication  and  division,  or  the  finding  of  powers  and 
roots,  are  greatly  facilitated  by  the  use  of  logarithms. 
When,  for  example,  it  is  necessary  to  compute  the  amount 
of  an  annuity,  i.e.,  of  a  series  of  equal  annual  payments,  of, 
let  us  say,  $10  each,  for  a  period  of  30  years,  accumulating 
at  a  rate  of  6%  compound  interest,  the  work  of  doing  this 
by  the  usual  arithmetical  process  is  exceedingly  laborious. 
Thus,  the  computations  for  the  first  three  years  are  as 
follows : 

First  annual  payment $10.00 

Xl.06 


6000 
1000 

Amount  at  end  of  1st  year $10.60 

Add  2nd  annual  payment 10.00 

Principal  at  beginning  of  2nd  year $20.60 

X  1.06 


12360 
.      2060 

Amount  at  end  of  2nd  year $21.836 

172 


LOGARITHMS    AND    THEIR    USE 


Amount  at  end  of  2nd  year  (brought  forward).  $21.  836 
Add  3rd  annual  payment  ....................       10.00 


Principal  at  beginning  of  3rd  year $31.836 

X  1.06 


191016 
31836 

Amount  at  end  of  3rd  year $33.74616 

One  can  readily  see  that  to  carry  this  on  for  the  full  30 
years  would  be  a  burdensome  task.  Hence  a  shorter  method 
is  desirable.  It  will  be  noted  that  the  amount  of  the  fund 
at  the  end  of  each  year  is  obtained  by  multiplying  it  by  the 
ratio  of  increase,  1.06,  which  gives  the  same  result  as  is 
secured  by  first  finding  the  interest  by  multiplying  the  prin- 
cipal at  the  beginning  of  each  year  by  .06,  and  then  adding 
this  to  the  principal  to  find  the  amount  at  the  end  of  the 
year.  Therefore,  if  we  wish  to  find  the  amount  of  $10  when 
placed  at  compound  interest  at  6%  for  30  years,  our  work 
will  be  abbreviated  by  first  multiplying  1  by  1.06  thirty  times, 
and  then  finding  the  product  of  $10  multiplied  by  the  result, 
which  may  be  expressed  thus : 

$10  X  1.0630 

In  case  of  an  annuity  of  $10  for  30  years  the  problem  is 
somewhat  more  complicated,  because  there  is  not  merely 
one  sum  of  $10  accumulating  at  compound  interest,  but  a 
series  of  annual  instalments  of  that  amount,  each  drawing 
interest.  In  a  30-year  period,  if  the  first  of  the  30  annuities 
is  pai'd  at  the  beginning  of  the  first  year,  it  will  have  a  period 
of  30  years  during  which  to  accumulate.  The  last  instal- 
ment will  be  paid  at  the  beginning  of  the  30th  or  last  year, 
and  each  one  will  draw  interest;  but  since  the  last  one  has 
only  one  year  during  which  it  will  accumulate,  its  interest 
is  not  compounded. 


174 


PRINCIPLES    OF    DEPRECIATION 


On  the  other  hand,  if  the  first  of  the  30  annuities  is  paid 
at  the  end  of  the  first  year,  it  will  have  not  30,  but  29  years 
during  which  to  accumulate,  and  the  last  annuity,  being  paid 
at  the  end  of  the  30th  year,  accumulates  no  interest  at  all. 
This  is  an  important  distinction,  and,  as  depreciation  allow- 
ances for  the  year  must  be  made  as  of  the  end  of  the  year 
and  not  at  the  beginning — for  the  depreciation  accrued  dur- 
ing the  year — calculations  must  in  such  a  case  be  based  on 
the  fact  that  the  last  annuity  bears  no  interest  and  the  first 
one  bears  interest  from  the  end  of  the  first,  or,  what 
amounts  to  the  same  thing,  from  the  beginning  of  the  sec- 
ond year.  This  must  be  kept  in  mind  in  the  discussion  of 
the  sinking  fund  formula  in  Chapter  XIII. 

Assuming,  then,  that  the  first  of  the  annuities  or  instal- 
ments of  $10  each,  begins  to  accumulate  interest  at  the  end 
of  the  first  year,  at  6%,  it  is  evident  that  it  will  accumulate 
interest  for  29  years,  and  will  amount  to : 

$10  X  1.0629 

Similarly  the  next  annuity  will  accumulate  to : 

$10  X  LOG28 

and  so  on,  until  we  come  to  the  next  to  the  last  instalment, 
which  will  accumulate  to : 

$10  X  1.06 

and  the  last  one,  which  will  have  no  time  to  accumulate  any 
interest  whatever.  Briefly,  each  annuity  accumulates  to  1.06 
times  the  amount  to  which  the  one  immediately  following 
accumulates.  Thus  we  have  a  series  of  amounts,  increasing 
or  decreasing  by  a  common  ratio,  depending  upon  which 
way  we  view  it,  exactly  the  same  as  the  series  discussed  in 
Chapter  XIII,  whose  sum,  V ' ,  is  expressed  by  the  following 
formula : 


LOGARITHMS    AND    THEIR    USE 


(r-l) 

in  which  x  is  the  annuity,  r  is  1  plus  the  rate  of  interest,  and 
n  the  number  of  years.  Therefore  the  accumulations,  at 
compound  interest,  of  an  annuity  of  $10,  for  30  years  at 
Qc/c,  the  first  annuity  being  paid  at  the  end  of  the  first  year, 
is  expressed  thus: 


1.06  —  1 

Principle  of  Logarithms 

A  short  method  of  making  the  computation  indicated  by 
1.0630,  which  is  read  as  1.06  raised  to  the  30th  power,  or 
simply  as  1.06  to  the  30th  power,  will  be  found  in  the  use 
of  logarithms.  To  understand  this  use  a  study  of  the  under- 
lying principle  upon  which  logarithms  are  based  will  be 
necessary. 

We  can  raise  any  number  to  any  desired  power  by  multi- 
plying itself  by  itself  the  required  number  of  times;  thus 
23  means  2  X  2  X  2,  or  8 ;  34  means  3  X  3  X  3  X  3,  or  81 ; 
44  means  4X4X4X4,  or  256,  and  so  on.  From  what 
has  just  been  said  the  following  is  self-evident. 

3  to  1st  power  is  3 

3  "  2nd  "  "  9 

3  "  3rd  "  "  27 

3  "  4th  "  "  81 

3  "  5th  "  "  243 

3  "  6th  "  "  729 

3  "  7th  ;"  "  2187 

3  "  8th  "  "  6561 

3  "  9th  "  "  19683 

3  "  10th  "  "  59049 


PRINCIPLES     OF    DEPRECIATION 

and  so  on.  The  numbers  in  the  second  column  are  the 
indices,  indicating  the  power  to  which  3  is  raised  to  secure 
the  number  in  the  third  column.  Thus,  39  =  19683; 
35  =  243. 

Now  suppose  that  we  desire  to  multiply  243  by  81.  By 
ordinary  multiplication,  243  X  81  =  19683.  From  the 
foregoing  table  it  may  be  seen  that  243  =  35,  and  81  =  3*. 
By  a  principle  of  mathematics  known  as  the  law  of  indices, 
35  X  34  =  35+4  =  39.  That  is,  35  is  multiplied  by  34  by  sim- 
ply adding  together  the  indices.  That  this  is  correct  may 
be  seen  by  a  glance  at  the  table.  There  we  find  that  39  equals 
19683,  as  we  have  already  found  by  multiplication.  Con- 
versely, 243-^81  =  35-i-34  =  35-4  =  31*=3;  for  3  raised 
to  the  5th  power  is  243,  and  this  amount,  243,  divided  by 
34,  or  81,  gives  3.  Thus,  in  a  very  simple  way,  we  have 
substituted  addition  and  subtraction  for  multiplication  and 
division. 

Let  us  suppose  further  that  we  desire  to  extract  the 
square  root  of  59049.  As  will  be  seen  from  the  table,  this 
is  3  raised  to  the  10th  power,  or  310.  The  square  root  of 
59049  is  therefore  the  same  as  the  square  root  of  310. 
According  to  the  law  of  indices,  dividing  the  index  of  a 
number  by  2  is  equivalent  to  extracting  the  square  root. 
Therefore,  3^,  or  35,  is  the  square  root  of  310.  According 
to  our  table  35  =  243.  That  this  is  the  square  root  of 
59049  may  be  seen  by  multiplying  243  by  243,  which  equals 
59049.  By  reversing  the  procedure  a  number  may  be  raised 
to  any  power  by  simply  multiplying  its  index  by  that  power. 
Thus  243,  or  35,  may  be  squared  by  multiplying  5,  the 
index  of  3,  by  2  ;  thus  2432  =  35  x  2  =  310  =  59049.  Similarly 
39  =  19683. 


The  Logarithm 

In  the  table  given  on  page  175,  the  numbers  in  the  second 


LOGARITHMS    AND    THEIR    USE 

column  are  said  to  be  the  logarithms  of  the  numbers  in  the 
third  column  to  the  base  3.  In  other  words,  the  logarithm 
of  a  number  is  the  power  to  which  its  base  must  be  raised 
to  produce  that  number.  Thus,  8  is  the  logarithm  of  6561 
to  the  base  3,  and  2  is  the  logarithm  of  9  to  the  base  3. 

We  have  here  selected  the  number  3  as  a  base.  Any 
number  may  be  so  employed.  The  number  10  is  the  base 
usually  taken,  and  forms  the  basis  of  the  common  system  of 
logarithms.1  Therefore  common  logarithms  of  numbers  are 
indices  indicating  the  power  to  which  10  must  be  raised  to 
equal  those  numbers,  just  as  in  our  table  they  were  indices 
of  3. 

Since  most  numbers  are  not  integral  powers  of  10,  it 
follows  that  their  logarithms  are  integers  only  in  the  rare 
cases  that  they  are  integral  powers  of  10.  Thus,  102  =  100 ; 
therefore  2  is  the  logarithm  of  100  to  the  base  10.  Similarly 
3  is  the  logarithm  of  1000  to  the  base  10,  and  4  is  the 
logarithm  of  10000  to  the  base  10.  But  the  logarithm  of 
500  must  be  something  more  than  2  and  less  than  3;  that 
is,  it  is  2  plus  a  decimal.  A  five-place  logarithm  table  gives 

this  decimal  part  of  the  logarithm  to  five  points,  as 

69897 

A  six-place  table  gives  it  as 698970 

A  thirteen-place  table  gives  it  as. .    .6989700043360 

A  twenty-place  table  gives  it  as. .   .69897000433601880479 

Usually  the  last  figure  is  not  exactly  correct,  being  ap- 
proximated or  rounded  off  just  as  we  round  off  $18.217 
to  $18.22. 

The  Characteristic 

The  integral  part  of  a  logarithm  is  known  as  the  char- 


1  Any  good  table  of  common  logarithms  such  as  those  appearing  in  mathematical 
textbooks  may  be  referred  to  in  connection  with  the  problems  presented  in  this 
volume. 


j-rg  PRINCIPLES    OF    DEPRECIATION 

acteristic  of  the  logarithm.  Thus  the  logarithm  of  500  to 
the  sixth  place  is  2.698970,  and  therefore  the  characteristic 
of  the  logarithm  of  500  is  2.  Similarly  the  characteristic  of 
the  logarithms  of  all  numbers  from  100  to  999,  inclusive,  is 
2;  for  the  logarithm  of  100  is  2,  the  logarithm  of  999  is 
2.999565,  and  the  logarithms  of  all  numbers  between  100 
and  999  lie  between  2  and  2.999565. 

The  logarithm  of  1000  is  3,  for  103  =  1000.  The  loga- 
rithm of  9999  is  3.999957.  Therefore  the  characteristic  of 
the  logarithms  of  all  numbers  from  1000  to  9999  is  3,  and 
so  on.  It  will  be  noted  that  the  characteristic  of  any  loga- 
rithm is  determined  by  the  position  of  the  decimal  point  in 
its  number,  being  independent  of  the  digits  of  the  number. 
Thus,  the  characteristic  of  the  logarithm  of  7,  which  has 
one  unit  figure,  is  zero;  of  the  logarithm  of  77.77,  which 
has  one  figure  to  the  left  of  the  unit  place,  is  1 ;  of  the  loga- 
rithm of  9.3,  with  one  unit  figure,  is  0 ;  of  the  logarithm  of 
3742.17,  with  three  figures  to  the  left  of  the  unit  place,  is  3  ; 
of  the  logarithm  of  56689.778,  with  five  figures  to  the  left 
of  the  unit  place,  is  4 ;  and  so  on.  Hence,  to  find  the  char- 
acteristic of  the  logarithm  of  a  number,  this  rule  is  given : 

To  find  the  characteristic  of  the  logarithm  of  a  number, 
find  how  many  places  the  first  significant  figure  is  removed 
from  unit's  place.  This  determines  the  characteristic,  and 
it  is  positive  or  negative  (plus  or  minus)  accordingly  as  the 
first  significant  figure  is  to  the  left  or  right  of  unit's  place. 
Thus : 
Characteristic  of  the  logarithm  of  1.  is  0 

"    "  "         "         0.1          "  I  (minus  1) 

"  "    "  "          "       22.0  "  1 

"  "    "  "          "  .0222     "  2 

"  "    "  "         "     275.0          "  2 

"  "    "  "          "  .0004    "  4 

"  "    "  "         "  1785.27968  "  3 


LOGARITHMS    AND    THEIR    USE 


I79 


The  Mantissa 

The  mantissa  of  the  logarithm  of  a  number  is  the  deci- 
mal portion,  and  does  not  depend  upon  the  location  of  the 
decimal  point  but  upon  the  digits  of  which  the  number  is 
composed.  Thus,  while  the  characteristics  of  the  logarithms 
of  999,  99.9  and  9.99  are  2,  1,  and  0,  respectively,  the  man- 
tissa is  the  same  for  all,  viz.,  .999565.  Again,  the  charac- 
teristic of  the  logarithms  of  327,  729,  and  211  is  2  in  each 
case,  but  the  mantissas  are  .514548,  .862728,  and  .324282. 
While  the  characteristic  is  positive  or  negative,  depending 
upon  the  position  of  the  decimal  point,  the  mantissa  is 
always  positive.  The  mantissa  is  found  by  the  use  of  a  table 
of  logarithms. 

Finding  the  Logarithm  of  a  Number 

The  number  being  given,  its  logarithm  is  determined  by 
first  finding  the  characteristic  by  the  rule  given.  The  man- 
tissa is  found  from  a  table  of  logarithms,  as  follows : 

1.  When  the  number  is  composed  of  not  more  than  four 
figures : 

In  the  first  column  of  the  table  of  logarithms  find  the 
first  two  or  three  or  four  figures  of  the  number  (according 
to  the  table  used),  then  follow  across  on  the  same  line  until 
the  column  is  reached  headed  by  the  same  figure  as  the  last 
digit  in  the  number  whose  logarithm  we  wish  to  find.2  The 
decimal  so  found  is  the  mantissa.  To  avoid  repetition  in 
the  table,  the  first  two  (sometimes  three  or  four)  figures  of 
the  mantissa  are  printed  at  intervals  only,  in  the  second 
column. 

Find  log  37.53.  By  the  rule  the  characteristic  is  1.  In 
the  first  column  of  the  table  of  logarithms,  find  375,  and  on 
the  same  line  in  the  column  headed  by  last  digit  3,  is  found 


*  A  six-place  table  is  employed  in  the  computations  which  follow. 


!8o  PRINCIPLES    OF    DEPRECIATION 

the  mantissa  .574379.      As  the  characteristic  is  1,  the  loga- 
rithm of  37.53  is  1.574379.     Similarly: 

Log     727.4 2.861773 

Log  3256 3.512684 

Log  7274.0 3.861773 

2.  When  the  number  is  composed  of  more  than  four 
figures : 

By  glancing  at  the  table  of  logarithms  it  will  be  seen 
that,  within  certain  limitations,  the  numbers  are  propor- 
tional to  their  logarithms,  and  vice  versa.  Thus : 

Log  4290 3.632457, 

{difference  is  .000102 

"     4291 3.632559, 

"  .000101 
"  4292 3.632660 

"  .000101 
4293....  3.632761 

Thus,  while  the  difference  between  the  numbers  is  constantly 
1,  the  difference  between  the  logarithms  is  nearly  constant. 
These  differences,  102,  101,  and  101,  are  known  as  the 
tabular  differences?  and  their  almost  constant  amount  cor- 
responds in  a  very  close  degree  to  the  difference  of  unity 
between  the  numbers.  The  logarithms  are  therefore  nearly 
proportional  to  their  corresponding  numbers,  and  may  be 
assumed  to  be  exactly  proportional  to  them  for  practical 
purposes.  Consequently,  if  any  one  of  the  numbers  be  in- 
creased by  0.1,  its  corresponding  logarithm  will  be  increased 
by  .1  of  the  tabular  difference  between  the  logarithm  of  that 
number  and  the  logarithm  of  the  next  higher  number.  Thus : 

Log  4290.1  =  3.632467   (or  3.632457  +  .1  of  102) 

*  In  practice  the  ciphers  preceding  the  difference  figures  in  the  mantissas  are 
disregarded  to  save  time  and  space,  but  care  must  be  taken  in  the  interpolation 
process  to  add  the  differences  in  their  proper  places  to  the  right  of  the  decimal 
point. 


LOGARITHMS    AND    THEIR    USE  jg! 

Log  4290.2  =  3.63247?   (or  3.632457 +  .2  of  102) 
"     4290.9  =  3.632549   (or  3.632457 +  .9  of  102) 

This  process  of  finding  logarithms  of  numbers  between 
two  numbers  in  the  table  is  called  interpolation.  To  lessen 
the  work,  in  some  tables  the  tabular  differences  are  inserted 
in  a  separate  column,  and  at  the  bottom  of  the  page  is  some- 
times given  the  proportional  part  of  the  last  figure.  Thus, 
if  the  tabular  difference  is  102,  the  additions  to  be  made  for 
.1,  .2,  .3,  .4,  and  so  on,  are  10,  20,  31,  41,  and  so  on.  Had 
the  number  whose  logarithm  was  to  be  found  been  42901 
instead  of  4290.1,  the  mantissa  would  have  been  the  same, 
but  the  characteristic  would  have  been  4  instead  of  3. 

If  the  number  is  composed  of  six  figures,  as  429015,  and 
a  five-place  table  is  used,  the  correction  for  the  last  two 
figures  is  found  by  interpolation  as  indicated  above.  The 
correction  for  the  fifth  figure  is  .1  of  102,  or  10,  and  the 
correction  for  sixth  figure  is  .05  of  102,  or  5 ;  hence  15  must 
be  added  to  3.632457,  the  logarithm  of  4290,  which  gives 
5.362472  for  the  logarithm  of  429015. 

Finding  the  Number  Corresponding  to  a  Logarithm 

Given  the  logarithm  of  a  number,  the  number  itself  may 
be  discovered  by  the  use  of  a  table  of  logarithms.  First, 
from  the  characteristic  of  the  logarithm  the  position  of  the 
decimal  point  is  determined,  the  operation  being  simply  the 
reverse  of  that  employed  in  finding  the  characteristic.  Thus, 
if  the  characteristic  is  always  the  same  as  the  number  of 
place's  the  first  significant  figure  is  removed  from  unit's 
place,  it  follows  that  in  the  number  corresponding  to  a  given 
logarithm  the  number  of  places  the  first  significant  figure 
is  removed  from  unit's  place  will  depend  upon  the  charac- 
teristic, being  to  the  left  or  right  of  unit's  place  accordingly 
as  the  characteristic  is  positive  or  negative. 


PRINCIPLES     OF    DEPRECIATION 

Now  if  the  mantissa  appears  in  the  table,  the  correspond- 
ing number  is  found  immediately.  Thus,  to  find  the  number 
whose  logarithm  is  2.791059,  we  find,  by  reference  to  a 
table  of  logarithms,  that  the  corresponding  number  is  618.1, 
the  position  of  the  decimal  point  being  determined  as  noted 
above. 

If,  however,  no  mantissa  is  found  in  the  tables  in  exact 
agreement  with  the  mantissa  whose  number  we  wish  to 
find,  the  first  four  figures  of  the  mantissa  are  found,  and 
then  by  the  principle  of  proportional  parts  additional  figures 
can  be  added.  Thus,  to  find  the  number  whose  logarithm  is 
1.325220,  we  turn  to  the  table  and  find  that  this  mantissa 
lies  between  .325105  and  .325310.  We  now  proceed  as 
follows  : 

Mantissa  of  log  of  2115  =  .325310 

"     "     "    2114  =.325105 

Differences  1  205 

Mantissa  of  log  of  required  number  —  .325220 

"     "     "  2114  =  .325105 

Differences  (  ?)  115 

By  the  principle  of  proportional  parts, 
(?)  :1  ::  115:  205 

115 
or        ?==- 


the  figures  which  must  be  annexed  to  2114  to  give  the  num- 
ber whose  logarithm  is  1.325220.  Thus  the  required  num- 
ber is  21.145609+,  the  decimal  point  being  determined  by 
the  characteristic,  which  is  1.  Beyond  the  first  three  addi- 
tional figures  obtained  by  interpolation,  their  accuracy  can- 
not be  depended  on,  so  that  the  sixth  place  is  the  last  one 


LOGARITHMS    AND    THEIR    USE 


;i83 


to  be  retained.  Instead  of  using  the  phrase,  "number  whose 
logarithm  is  1.32522,"  the  following  briefer  expression, 
"log-1  1.32522,"  is  commonly  employed.  Thus : 

Log-1  2.75631  =  570.571 
Log-1     .00352=      1.00814 

Finding  Powers  and  Roots  of  Numbers 

In  the  first  part  of  this  chapter  we  have  seen  the  neces- 
sity of  a  convenient  method  of  finding  high  powers  of  num- 
bers in  making  interest  computations.  Thus,  an  annuity  oi 
$10,  at  Q%  compound  interest,  amounts  in  30  years  tos 

10(1.063Q-1) 
1.06  —  1 

The  reduction  of  this  rather  complex  form  necessitates  the 
raising  of  1.06  to  the  30th  power,  which  is  an  extremely 
tedious  process  by  multiplication.  Since  the  multiplication 
of  the  logarithm  of  a  number  by  a  given  number  has  the 
same  effect  as  raising  that  number  to  the  power  indicated 
by  the  given  number,  the  following  process  should  be  care- 
fully studied : 

Log  1.06=    .025306 
.025306X30=    .759180 
Log-1  .759180  =  5.74354 

which  is  the  30th  power  of  1.06. 

In- the  same  way  that  any  desired  power  of  a  number 
may  be  found  by  multiplying  its  logarithm  by  the  number 
representing  the  desired  power  and  then  finding  the  number 
in  the  table  corresponding  to  the  logarithm  represented  by 
the  product,  so  any  desired  root  of  a  number  may  be  found 
by  dividing  the  logarithm  of  that  number  by  the  number 


PRINCIPLES    OF    DEPRECIATION 

indicating  the  root  to  be  found,  and  then  finding  the  num- 
ber in  the  table  whose  logarithm  is  the  quotient. 
Find  the  30th  root  of  5.74354. 

Log  5.74354=    .759179 
.759179-^30  =    .0253059 
Log-1  .0253059  =  1.06 

which  is  the  30th  root  of  5.74354. 

Referring  again  to  the  problem  in  hand,  and  substituting 
5.74354  in: 


1.06  —  1 

we  find  its  value  to  be  $790.59,  the  amount  of  the  annuity 
of  $10,  at  Q%  compound  interest,  for  30  years. 


CHAPTER    XVIII 

SELECTED   BIBLIOGRAPHY 

The  references  given  herewith  are  only  to  such  books 
and  articles  as  it  is  believed  will  be  most  useful  to  the  student 
making  a  general  study  of  the  subject  of  depreciation.  A 
very  complete  bibliography  may  be  found  in  volume  76  of 
the  Transactions  of  the  American  Society  of  Civil  Engi- 
neers, pages  2133-2193;  also  in  Whitten's  Valuation  of 
Public  Service  Corporations,  pages  735-745. 

BOOKS 

Dicksee,  L.  R.    Depreciation,  Reserves,  and  Reserve  Funds. 

80  pages.    London,  1912. 
Floy,  Henry.    Valuation  of  Public  Utility  Properties.    390 

pages.    New  York,  1912. 
Humphreys,  A.  C.    Lecture  Notes  on  Some  of  the  Business 

Features  of  Engineering  Practice.     565  pages.     Ho- 

boken,  N.  J.,  1912. 
Matheson,  Ewing.     The  Depreciation  of  Factories.     230 

pages.    London,  1910. 
Leake,    P.    D.      Depreciation   and   Wasting  Assets.      195 

pages.     London,  1912. 
Whitten,  R.  H.    Valuation  of  Public  Service  Corporations. 

798  pages.    New  York,  1912. 

ARTICLES 

• 
• 

Alvord,  John  W.  The  Depreciation  of  Public  Utility  Prop- 
erties as  Affecting  Their  Valuation  and  Fair  Return. 
Proceedings  American  Society  of  Civil  Engineers, 
Nov.,  1913.  pages  2045-2060.  Claims  that  deprecia- 

185 


PRINCIPLES    OF    DEPRECIATION 

tion   should   be   deducted    for   rate-making   purposes, 
unless  represented  by  a  definite  sinking  fund. 

Britton,  John  A.  Depreciation.  Progressive  Age,  June  15, 
1908,  Vol.  26,  page  379.  Cites  several  court  decisions 
substantiating  the  inclusion  of  depreciation  as  an 
operating  expense. 

Chase,  Harvey  S.  Maintenance  and  Depreciation  Charges 
in  Accounts  of  Public  Service  Corporations.  Journal 
of  Accountancy,  May,  1907,  Vol.  4. 

Cooley,  M.  E.  Factors  Determining  a  Reasonable  Charge 
for  Public  Utility  Service.  Journal  of  Western  Society 
of  Engineers,  Jan.,  1914,  pages  1-17. 

Duffy,  C.  N.  Depreciation.  Electric  World,  Feb.  1,  1908. 
Gives  details  on  electric  power  plants,  classifies  specific 
assets,  and  suggests  methods  of  handling  depreciation. 
Applies  to  Wisconsin  conditions.  See  editorial  in  same 
paper.  Same  article  in  Progressive  Age,  Sept.  1,  1909. 

Depreciation  Allowance  for  Income  Tax  (England). 
Journal  of  Gas  Lighting,  Nov.  23,  1909,  Vol.  108, 
pages  517,  518. 

Delano,  Frederick  A.  Application  of  a  Depreciation  Charge 
in  Railway  Accounting.  Journal  of  Political  Economy, 
Nov.,  1908,  Vol.  16,  pages  585-601. 

Geijsbeek,  J.  B.  Fair  Return  to  Public  Utilities.  Journal 
of  Accountancy,  Vol.  17,  April,  1914. 

Gillette,  H.  P.  Use  of  Depreciation  Data  in  Rate  Making: 
Electrical  World,  Nov.  2,  1912. 

Gray,  Henry  L.  Necessity  of  Depreciation  Reserves.  Rail- 
way Age  Gazette,  May  27,  1910,  page  1297. 

Grunsky,  C.  E.  The  Appraisal  of  Public  Service  Properties 
as  a  Basis  for  the  Regulation  of  Rates.  Transactions 
of  the  American  Society  of  Civil  Engineers,  Vol.  75, 
page  770.  Maintains  that  depreciation  should  not  be 
deducted  for  rate-making  purposes,  but  that  original 


SELECTED    BIBLIOGRAPHY 

investment   should   be  used   for  fixing  rates,   on   the 
theory  that  the  investment  must  be  maintained  intact; 
first,  by  the  maintenance  of  the  plant,  and,  second,  by  a 
sum  set  aside  for  renewals  from  time  to  time. 
Humphreys,  A.  C.    Depreciation.    Progressive  Age,  Dec.  2, 

1907,  Vol.    25,   pages   688-699.     A   criticism  of  the 
valuation  work  of  the  "so-called  experts." 

Humphreys,  A.   C.     Depreciation,  Estimated  and  Actual. 

Proceedings    of   the   American    Gas    Institute,    1913, 

Part  2,  pages  505-530. 
Jackson,  W.   B.     The  Depreciation   Problem.     Annals  of 

the  American  Academy  of  Political  and  Social  Science, 

Jan.,  .1911. 
Knight,  Alfred.    Depreciation  and  Other  Reserves.   Journal 

of  Accountancy,  Jan.,  1908,  Vol.  5,  pages  189-204. 
Mack,  Edwin  S.    Depreciation.    Progressive  Age,  June  15, 

1908,  Vol.  26,  pages  372-375. 

Neal,  J.  H.  Where  Maintenance  Ends  and  Depreciation 
Begins.  Proceedings  of  American  Street  and  Inter- 
urban  Railway  Accountant's  Association,  1907,  Vol.  2, 
pages  195-202. 

Obsolescence  of  Electric  Lighting  Plant.  Electrical  Review 
(London),  Sept  25,  1908,  Vol.  63,  pages  516,  517. 

Prouty,  Charles  A.  The  Work  Involved  in  the  Valuation 
of  Railroads.  Railway  Age  Gazette,  Feb.  13,  1914, 
Vol.  56,  pages  320-323. 

Riggs,  H.  E.  Valuation  of  Public  Service  Corporations 
Property.  Proceedings  of  the  American  Society  of 
Civil  Engineers,  Nov.,  1910. 

Staub,  Walter  A.  Deferred  Charges  to  Operating.  Journal 
of  Accountancy,  Oct.,  1909,  Vol.  8,  pages  401-418. 

Stockwell,  H.  G.  Depreciation  Renewal  and  Replacement 
Accounts.  Journal  of  Accountancy,  Dec.,  1909,  and 
Jan.,  1910,  Vol.  9,  pages  87-103,  189-210. 


1 88  PRINCIPLES    OF    DEPRECIATION 

Treatment  of  Depreciation  in  Connection  with  the  Federal 

Corporation   Tax.     Journal   of  Accountancy,   March, 

1912,  pages  218-222. 
Wilmot,  H.  W.     Depreciation.     Journal  of  Accountancy, 

Dec.,  1909,  Vol.  9,  pages  104-113. 
Wilgus,  W.  J.     Appraisal  of  the  Lehigh  Valley  Railroad. 

Engineering  Record,   May  30,   1914,  Vol.   69,  pages 

613-617.      Compiled    from   directions   issued   by   Mr. 

Wilgus  for  the  guidance  of  his  staff  in  the  appraisal  of 

the  Lehigh  Valley  Railroad. 


INDEX 


Accounts,  importance  of,  66,  67 
"Accrued  Amortization  of  Capital,"  73,  74 
Addie  &  Sons  v.  Solicitor  of  Inland  Revenue,  84 
Adjustments  in  plant  ledger,  45,  46 
Alterations,  15 
Amalgamated  Copper  Co., 

reserves  and  funds  in  balance  sheet,  59 
American  Tobacco  Co., 

reserves  and  funds  in  balance  sheet,  59 
Amortization  of  bonds  (footnote),  49 
Annuity  method  of  providing  for  depreciation,  127-129,  152-158 

graphic  illustration,  158 

table  of  computations,  157 
Anticipated  losses,  reserve  for,  89 
Appleton  v.  American  Malting  Co.,  68 
Appreciation,  109-119 

considered  as  income,  116,  117 

limited  by  Supreme  Court,  117 

of  land,  112-119 

B 

Bad  debts,  89 

Balance  sheet  accounts,  of  Interstate  Commerce  Commission,  73 

Balance  sheets, 

replacements  and  betterments  in,  27 

reserves  and  funds  in,  51,  55,  58,  59 
Baldwin  Locomotive  Works, 

reserves  and  funds  in  balance  sheet,  59 
Belfast  &  M.  L.  R.  Co.  v.  City  of  Belfast,  68,  69 
Bethlehem  Steel  Corporation, 

reserves  and  funds  in  balance  sheet,  58,  59 
Bibliography,  selected,  185-188 
Bonds  and  income  tax,  82,  90 
Bonnejr  v.  Bassett  Mines,  Ltd.,  85 
Buffalo,  Rochester  &  Eastern,  valuation  of,  32 
Buildings, 

allowance  for  depreciation  of,  84 

removal  of,  89 
Burnley  Steamship  Co.  v.  Aikin,  84 

189 


I90  INDEX 


Capital, 

preservation  of,  68 

twofold  character  of,  13 
Capital  assets,  sale  of,  89 
Capitalization,  93,  96,  107 

overcapitalization, 
prevention  of,  25 
result  of,  32 

Chancellor  of  Exchequer  on  Income  Tax,  80 
Characteristic  of  a  logarithm,  177,  178 
Character  of  industrial  plant,  13-33 
Circulating  capital,  13 

City  of  Beloit  v.  Beloit  Water,  Gas  and  Electric  Co.,  60,  61 
City  of  Knoxville  v.  Water  Co.,  32,  70,  84,  103 
City  of  Whitewater  v.  Whitewater  Electric  Lighting  Co.,  103 
Classification  of  depreciation  charges,  for  railroads,  75 
Clayton  v.  Newcastle-under-Lyme,  84 
Coltness  Iron  Co.  v.  Black,  81,  85 
Columbus  Ry.  &  Light  Co.  v.  City  of  Columbus,  103 
Commission  control,  21,  66-79,  95,  96,  103,  108-110,  113,  114 
Commissioner  of  Internal  Revenue,  regulations  of,  81,  84,  87-92 
Competition, 

and  rates,  93 

relation  to  income,  20 
Composite  depreciation,  23,  25,  31,  47,  65,  76,  132 

indicated  by  reserve,  47 
Compulsory  depreciation  charge,  78 
Consolidated  Gas  Co.  v.  City  of  New  York,  84,  116, 117 
Constituents  of  plant  value,  14 
Constitution  amended,  83 
Contingencies  an  element  of  cost,  16 
Corporate  organization,  13 
Corporations  concentrate  wealth,  14 
Corporation  Tax  Law  of  1909,  81-83 
Cost, 

developmental,  19 

direct,  15,  32 

engineering,  17,  32 

indirect,  16 

of  reproduction,  99-105 

unusual  interpretation  of,  114,  115 
Courts,  control  by,  66-79,  103,  113 


INDEX  I9I 

Cramp  &  Sons,  Wm., 

reserves  and  funds  in  balance  sheet,  59 
Current  repairs, 

an  expense,  32 

not  adequate,  25 

not  part  of  depreciation,  23 

D 

Decisions, 

on  depreciation,  32,  69,  70 
on  income  tax,  81,  84-87 
on  valuations,  103,  108,  110,  113,  117,  118 
Depreciation, 

actual,  132,  133 

and  efficiency,  60-65,  102 

and  income  tax,  80-92 

and  rates,  101 

an  expense,  32 

a  proper  charge,  70,  71 

as  affected  by  point  of  view,  120,  121 

charge,  how  regulated,  71-78 

charges, 

classification  of,  for  railroads,  75 

purpose  of,  49,  50 
composite,  23,  25,  31,  47,  65,  76,  132 

always  occurs,  76 
compulsory  charge  to,  78 
decisions  on,  32,  69,  70 
deduction  from  income  tax,  81,  84-92 
defined,  62 

functional,  22,  28,  29,  31 
fund,  48,  50-53,  55-59 

formation  of,  55,  56 
inadequate  allowance  for,  108 
in  valuations,  97-99 
methods  of  providing  for,  120-171 

annuity  method,  127-129,  152-158 

•equal  annual  payment  method,  129,  130,  159-165 

reducing  balance  method,  124,  125,  138-144 

sinking  fund  method,  77,  125-127,  145-151 

straight  line  method,  123,  124,  134-137 

unit  cost  method,  130-132,  166-171 
of  indirect  costs,  31,  32 
of  mines,  85-87,  92 


192 


INDEX 


Depreciation — Continued 

on  basis  of  averages,  108 
physical,  22,  28,  29,  31 

adjustments  for,  45,  46 

requirements  of  Interstate  Commerce  Commission,  72-79 
reserve, 

and  plant  ledger,  46,  47 
formation  of,  54,  55 
how  handled,  26-28,  77 
use  of,  74,  90 
vs.  fund,  49-59 
unit,  23,  24 

Developmental  costs,  19 
Direct  costs-  15,  32 

E 

Educational  period,  20 
Efficiency, 

defined,  61 

depreciation  and,  60-65,  102 

not  to  be  impaired,  65 

Electrical  corporations,  uniform  system  of  accounts  of,  74 
Electric  railways,  uniform  system  of  accounts  of,  74 
Engineering  as  a  cost,  17,  32 
English  income  tax,  80,  81 

Equal  annual  payment  method  of  providing  for  depreciation,  129, 
130,  159-165 

graphic  illustration,  164 

table  of  computations,  162-163 
Equipment,  15 

Equitable  basis  of  rate-making,  105 
Excise  Tax  of  1909,  81-83 
Exhaustion, 

allowance  for,  84-88,  91,  92 

of  mines,  84-88,  91,  92 
Expenditures,  capitalized,  15,  20 

F 

Factors  of  value,  61 

Finance  Act  (English),  of  1907  and  1910,  80 
Fixed  assets,  13 
Franchises,  21,  94,  95 
Functional  depreciation,  22,  28,  29,  31 


INDEX  IQ3 


Fund,  depreciation, 

advisability  of  creating,  57,  58 

depreciation  reserve  vs.,  49-59 

formation  of,  55,  56 

use  of,  48 
Fund,  sinking  (See  "Sinking  Fund") 

G 

Gas  companies,  74,  96 
;<General  Amortization,"  73 
General  Electric  Co., 

reserves  and  funds  in  balance  sheet,  59 
Good-will,  89 

H 

Hughes,  Justice,  on  appreciation,  117,  118 
Hydroelectric  plant,  analysis  of,  34-38 


Illinois  Central,  valuation  of,  115 

Inadequacy,  22,  29,  30,  62 

Incidental  costs,  15 

Income  accounts,  of  Interstate  Commission,  73 

incomes,  how  fixed,  20,  21 

Income  tax,  80-92 

anticipated  losses,  89 

bad  debts,  89 

bonds,  82,  90 

decisions,  84-87 
in  England,  81,  84 

deductions,  81-92 

depreciation,  81,  84-92 

depreciation  reserve,  90 

exhaustion,  84-88,  91,  92 

good-w,ill,  89 

incidental  repairs,  90 

in  England,  80,  81,  84 

interpretation  of  law,  87,  88 

mineral  deposits,  84-88,  91,  92 

of  1913,  83,  87 

patents,  91 

real  estate,  82 


194 


INDEX 


Income  tax — Continued 

regulations  of  Commissioner  of  Internal  Revenue,  81,  84,  87-92 

regulations  of  Treasury  Department,  82,  90,  92 

removal  of  buildings,  89 

sale  of  capital  assets,  89 

stocks,  82 

timber  land,  91 
Indirect  costs, 

depreciation  of,  31,  32 

in  valuations,  16 
Industrial  plant  (See  also  "Plant  Ledger") 

analysis  of,  35 

character  of,  13-33 
Industry,  State's  relation  to,  66,  93 
In  re  London,  etc.,  Bank,  67 
Insurance,  15 

during  construction,  18,  32 

method,  77 
Interborough  Rapid  Transit  Co., 

reserves  and  funds  in  balance  sheet,  58,  59 
Interest,  15 

and  funds,  52-54,  57 

computing,  172-175 

during  construction,  18,  32 

in  depreciation,  125 

on  investment,  127-129 
International  Harvester  Co., 

reserves  and  funds  in  balance  sheet,  59 
International  Paper  Co., 

reserves  and  funds  in  balance  sheet,  58 
Interstate  Commerce  Commission, 

accounts  required  by,  72-76 

and  depreciation  charge,  62,  71 

and  land  valuations,  113,  114 

approves  insurance  method,  77 

basis  suggested  to  estimate  depreciation,  74 

recognizes  indirect  costs,  16-18 

rejects  funds,  57 

requirements  for  railroad  companies,  74-77 

work  of,  69-78 
Investment, 

relation  of  unit  cost  to,  37 

to  be  preserved,  64,  65 

vs.  income,  20 


INDEX 
Investor,  how  protected,  21,  32 

K 

Kennebec  New  Gravity  Water  Supply,  engineering  costs  in,  17 
Knowles  v.  Me  Adam,  81,  85 
Knoxville  v.  Water  Co.,  32,  70,  84,  103 

L 

Land, 

and  rate-making,  112,  113 

in  valuations,  112-119 

attitude  of  Interstate  Commerce  Commission,  113 
court  decisions,  113,  117,  118 

not  a  wasting  asset,  112 

not  "used  and  useful,"  113,  119 
Leases,  investment  in  may  be  diminished,  33 
Ledger,  plant  (See  "Plant  Ledger") 
Lee  v.  Neuchatel  Co.,  33 
Lehigh  Valley  Railroad  Co., 

reserves  and  funds  in  balance  sheet,  59 
Lehigh  Valley  Railroad  valuation,  118 
Little  Miami,  etc.,  R.  R.  v.  U.  S.,  84 
Logarithms  and  their  use,  172-184 
Losses,  anticipated,  reserve  for,  89 
Louisville  sewerage  works,  engineering  costs  in,  17 

M 

Machinery,  allowance  for  depreciation  of,  24,  84 

Mantissa  of  a  logarithm,  179 

Massachusetts, 

board  of  railway  commissioners,  96,  103 

gas  and  electric  light  commission,  96 
Metropolitan  reorganization  case,  101,  103,  107 
Metropolitan  Water  Works,  engineering  costs  in,  17 
Michigan,  valuations  in,  108 
Millejr  v.  Fairie,  85 
Mines,  exhaustion  of,  84-88,  91,  92 
Mining  corporations, 

and  income  tax,  $4-88,  91,  92 

investment  may  be  diminished,  33 
Minneapolis  Western  Railway,  valuation  of,  109 
Minnesota  Railway  and  Warehouse  Commission,  96,  109,  114 
Minnesota  Rate  Cases,  117,  118 


I96  INDEX 

Monopoly,  21 

Mortality  tables  of  structures,  108,  109 

N 

Natural  deposits,  91,  92 
Net  profits,  meaning  of,  67-70 
New  York,  New  Haven  and  Hartford,  103 
New  York  Public  Service  Commission,  96 

on  appreciation,  110,  117 

on  depreciation  charge,  62 

system  of  accounts,  72,  74 

New  York  Water  Works,  engineering  costs  in,  17 
Northern  Pacific,  109 


Obsolescence,  22,  29,  62,  84,  107,  122 

Operating  expenses,  classification  of  by  Interstate  Commerce  Com- 
mission, 74,  76 
Overcapitalization, 

preventing,  25 

result  of,  32 
Overhead  costs,  32 


Park  v.  Grant  Locomotive  Works,  67 
Patents, 

and  income  tax,  91 

investment  in  may  be  diminished,  33 
People  v.  Roberts,  33 
Philadelphia  Rapid  Transit  Co., 

reserves  and  funds  in  balance  sheet,  58,  59 
Physical  depreciation,  22,  28,  29,  31 

adjustment  for,  45,  46 

Pioneer  Telephone  and  Telegraph  Co.  v.  Westenhaver,  103 
Pit  sinking,  allowance  for,  84,  85 
Pittsburgh  Brewing  Co., 

reserves  and  funds  in  balance  sheet,  58 
Plant,  industrial  (See  "Industrial  Plant") 
Plant  ledger,  39-48 

adjustments  in,  45,  46 

character  of,  39 

description  of,  39,  40 

how  controlled,  46,  47 


.  INDEX 

Plant  ledger — Continued 

illustrated,  42-44 

use  of,  41 

Plant  value,  constituetits  of,  14 
Power  house  equipment,  analysis  of,  37 
Preliminary  costs,  15 
Preliminary  expenses,  17,  18 
Present  value  vs.  cost-of-reproduction,  99 
Profits,  net,  67-70 
Promoter,  work  of,  14 
Property,  sale  of,  89 

Public  service  commissions,  62,  72,  74,  95,  96,  110,  117 
Public  utilities,  93-95 

Q 

Queens  Borough  Gas  and  Electric  case,  108,  117 

R 

Railroad  accounts,  required  by  Interstate  Commerce  Commission, 

74-77 

Railroad  commissions,  95,  96,  103,  108-110,  114 
Railroad  Securities  Commission,  110 
Rate-making,  93,  96,  101-108,  112 
Real  estate  and  income  tax,  82 
Reducing  balance  method  of  providing  for  depredation,  124,  125, 

138-144 

graphic  illustration,  143 
table  of  computations,  142 
Regulation  by  courts  and  commissions,  21,  66-79,  95,  96, 103, 108-110, 

113,  114 
Renewals, 

and  repairs,  76 
not  adequate,  25 
Repairs, 

and  renewals,  76 
Current, 

an  expense,  32 
not  adequate,  25 
not  part  of  depreciation,  23 
incidental,  90 
Replacements, 

an  expense,  32 
depreciation  and,  23-33 


198  INDEX 

Replacements — Continued 

relation  of  reserve  to,  47 

reserve,  26 

Reproduction-cost-new,  16,  101-105 

Reproduction  method,  114,  115,  118  (See  also  "Valuations") 
Re  Queens  Borough  Gas  and  Electric  Co.,  108,  117 
"Reserve  for  Accrued  Depreciation,"  57 
Reserve  for  anticipated  losses,  89 
Reserve  for  depreciation, 

and  plant  ledger,  46,  47 

formation  of,  54,  55 

how  handled,  26-28,  77 

purpose  of,  74,  90 

relation  to  replacements,  47,  48 

vs.  fund,  49-59 
"Road  and  Equipment,"  57 

S 

Sale  of  capital  assets,  89 
Sales  method  of  valuation,  115,  116 
Sears,  Roebuck  &  Co., 

reserves  and- funds  in  balance  sheet,  59 
Securities,  96 

Shepard  v.  Northern  Pacific  Ry.  Co.,  113 
Simpson  et  al.  v.  Kennedy,  117 
Simpson  et  al.  v.  Shepard,  117 
Simpson  et  al.  v.  Shillaber,  117 
Sinking  fund,  53 

formula,  54,  56,  57 

method  of  providing  for  depreciation,  77,  125-127,  145-151 
graphic  illustration,  150 
table  of  computations,  149 
Smith  v.  Westinghouse  Brake  Co.,  84 
Smyth  v.  Ames,  110 

Springfield  (Mass.)  Ludlow  filters,  engineering  costs  in,  17 
State's  relation  to  industry,  66,  93 
Steenerson  v.  Great  Northern  Ry.  Co.,  113 
St.  John  v.  Erie  Ry.  Co.,  69 
Stocks  and  income  tax,  82 
Straight  line  method  of  providing  for  depreciation,  123,  124,  134-137 

graphic  illustration,  137 

table  of  computations,  136 

Stratton's  Independence,  Ltd.,  v.  Howbert,  85-87,  92 
Street  railways,  uniform  system  of  accounts  of,  74,  95 


INDEX  I99 

Sub-stations,  analysis  of,  37 

Supreme  Court  decisions,  32,  69,  70,  113,  117,  118 

Surveys,  preliminary,  as  costs,  18,  32 

T 

Taft  v.  Railroad  Co.,  69 
Taxation  of  public  utilities,  93,  94,  97 
Taxes  as  cost,  32 

Tax,  income,  80-92  (See  also  "Income  Tax") 
Telegraph  corporations,  95 
Telephone  corporations,  95 
Terminology  of  reserves,  57 
Texas  Railroad  Commission,  96,  97 
Third  Avenue  Railway  Co., 

reserves  and  funds  in  balance  sheet,  58,  59 
Timber  land,  91 

Tin  mine  shaft,  allowance  for,  85 
Transmission  system,  analysis  of,  36,  37 
Treasury  Department  regulations,  82,  90,  92 

U 

Unearned  increment,  25 

Union  Pacific  R.  R.  v.  U.  S.,  69,  70 

Unit,  definition  of,  34 

Unit  cost,  relation  to  investment,  37 

Unit  cost  method  of  providing  for  depreciation,  130-132,  166-171 

Unit  depreciation,  23,  24 

United  Gas  Improvement  Co., 

reserves  and  funds  in  balance  sheet,  58 
United  States  Steel  Corporation, 

reserves  and  funds  in  balance  sheet,  58 
United  States  v.  Kansas  Pacific  Ry.  Co.,  70 
Utah  Copper  Co., 

reserves  and  funds  in  balance  sheet,  59 

V 

Valuation  problem,  96,  97 
Valuations,  93-111 

indirect  costs  in,  16 

land  in,  112-119 

decisions,  113,  117,  118 
Value,  factors  of,  61,  62 
Value,  plant,  constituents  of,  14 


200  INDEX 

W 

Washington,  valuations  in,  108,  109 

Wasting  assets, 'depreciation  of,  33  (See  also  "Mines") 

Water  companies,  95 

Wear  and  tear,  62,  122 

allowance  for,  84 
Wells,  Fargo  &  Co., 

reserves  and  funds  in  balance  sheet,  59 
Willcox  v.  Consolidated  Gas  Co.,  70,  113 
Wisconsin  Railroad  Commission,  61,  96,  103 
Wisconsin,  valuations  in,  108 


Sr^-nl  of 


Los  nicies  24,  California 


VHHfSS     ""1 


1 


ANGELES.  CAL.F. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below. 


wnv 


196f 


JAN     8    1962 


s 


NOV  6 


MAR     2  1974 

IMAR  2-3PM 


Form  L9-32m-8,'57(.C8680s4)444 


